Old Riga
Old Riga is the historical and geographical centre of Riga, located on the right bank of the Daugava River. . Old Riga (Latvian: Vecrīga) is famous for its old churches, cathedrals and monuments of medieval architecture (13th-18th century).
Here is the listing of some Old Town some main sights
Dome Cathedral National Architectural Monument, 1211, XIII-XX centuries The building of Dome Cathedral was started in 1211 and continued through many centuries. The 6768-pipe Dome organ is one of the largest organs in the world. It was built in the 80s of the XIX century.
Dome Square (Doma laukums in Latvian) is located in the center of old town, It is the largest square in Riga, Dome Cathedral is located here. Many events that are celebrated in Riga happen here. In the summer time (tourism season) there are open-air bars that are opened in the center of the square and live music.
The House of Blackheads is where the merchants-to-be had their guild. Part of this building is the tourist information office, the rest is a fascinating museum. The upper levels house grand ballrooms while the basement has a wine cellar and several exhibits relating to trading in Riga.
Town Hall – a three-storied building with a tower and a clock on it. The Riga City Council consisting of 60 councillors who are elected every 4 years is established on the basis of party factions. 
The Town Hall Square was formed of a market square and up to 19th century it was the economic and an administrative centre of Riga. A lot of different processions, competitions, tournaments and dances were organized on this square. The square was also a place for a fulfilment of execution.
The statue of Roland has been established in 1896 on the Town Hall square. Roland was considered to be fair judge, the defender of accused and fair executor of judgement. Therefore it has been established on the Town Hall square with its face turned to the direction of the Town Hall.
St. Peter's Church, dating to 1209, is Riga's oldest church. Besides its ensemble of architecture, the church has an elevator to the tower from where you can see all of Riga. The interior features early and late Gothic forms and the steeple is an extraordinary example of Baroque in Europe.
Convent Yard of the Holy Ghost (Konventa Sēta)
Originally there was the Castle of Knights of Sword Order (the so called White Stone Castle), which was destroyed in 1297. The castle was rebuilt on the embankment of the Daugava in the former site of the Holy Ghost Hospital (which therefore was rebuilt instead the ruins of the White Stone Castle). After some time this place was renamed as the Convent Yard of the Holy Ghost.
John’s Courtyard Bishop Albert’s first apartment and the first church were located. The first Latvian school was opened here at the end of the 16th century. In 1938, tearing down the buildings, the most ancient defence wall of the city was found. It was renovated 25 years later.
The church is built on the site of the palace of Bishop Albert of Riga (thirteenth century). In 1234 Dominican friars took responsibility for the original small chapel and dedicated it to St John the Baptist. It was extended around 1330, and continued as a Dominican chapel and parish church until 1523, and the Reformation. It continued as a parish church of the reformed Evangelical Lutheran Church. The church suffered severe damage in Riga's great city fire of 31 May 1677, but was repaired, with a new spire added
St. George’s Cathedral (White Stone Castle), 1207-1209, It was built from white dolomite around 1207 to become castle for the Master of the Knights of Sword Order, which was destroyed by the citizens of Riga in 1297 while struggling against the Order. One area of the castle remained unscathed where St. George’s Cathedral was located (later the Convent Yard of the Holy Ghost), which during the Reformation was used as a storage area. Without any significant changes the structure was used as a storage area until the end of XXth century when in 1989 the Museum of Applied Arts was established there.
Both Great Guild and Small Guild dates from the 14th century when Riga was a member of Hanseatic League. The Great Guild was for the merchants and the Small Guild was for the craftsmen. The appearance of the buildings you see today is of later date. The Great Guild was built between 1854 - 57 and today it houses the Latvian State Philharmonic Orchestra. The Small Guild was constructed between 1864 - 1866. Today the building is home of a cultural house, Guild. There are concerts, dances and conferences held here. 
Riga Castle (Rīgas pils) is a castle on the banks of River Daugava. The castle was founded in 1330. This structure was thoroughly rebuilt between 1497 and 1515. Upon the castle's seizure by the Swedes, they constructed spacious annexes in 1641. The fortress was continually augmented and reconstructed between the 17th and 19th centuries. Sometime in the 1930s, some renovation work was done. The Latvian government declared the castle its residence in 1938. Today it is the official residence of the President of Latvia as well as home to several museums.
The Powder Tower (Pulvertornis) and Fortifications Powder Tower is one part of the former fortification system, surrounding Riga. It was first mentioned in 1330 and it was originally called Smilsu Tornis (The Sand Tower), but from the 17th century when the powder had been kept in it, the Tower gained the name of Powder. The diameter of this round tower is 14.3m, height -25.6m, the width of the walls reaches 3m.The Powder Tower was restructured in the years 1937 to 1940 when it was included to the structure of the Latvian War Museum. 
Swedish Gate (Zviedru vārti), built in 1698 to celebrate the Scandinavians' occupation of the city, and the only such structure left in Old Riga. The apartment above belonged to the city executioner or bender, who would put a red rose on the window ledge on the morning before a head rolled
'Three Brothers' are the best examples of residential buildings of medieval Riga. The name of this architectural ensemble, which represents different development stages of medieval dwelling houses, when buildings were erected on narrow land plots, originated from a similar group of warehouses in Tallinn, bearing the name 'Three Sisters'. During the restoration, the backyards of all three buildings were united. Various stone portals from demolished houses were collected together, as well as the Riga Coat of Arms from the Blue Guard Armory, and were put into the walls of the yard. 
St. Jacob’s Church (Sv. Jekaba baznica) is the fourth largest church in the Old Town. St. Jacob’s Church was mentioned for the first time in written records in 1225. In those times the church was still outside the town and was designed for residents of the suburbs. Unlike other churches in Old Riga, the steeple of St. Jacob’s church has preserved its original Gothic shape as it was in ancient times. Today it is a Roman Catholic Cathedral.
The building of the Parliament (Saeimas nams) of the Latvian Republic has been constructed in 1867, as the Vidzemes Knightly house by the project of architect Robert Pflug and the first academically educated Latvian architect Janis Baumanis. In 1900 - 1903 the Knightly house has been expanded. In 1923 building has been reconstructed again, after what the first parliament of republic - the Saeima has begun its work in this building.
Jacob’s Barracks
The barracks were built in the 18th century and at those times it was the longest building in Riga. They are situated nowadays in Torna iela, a beautiful pedestrian street in Old Town with the Riga City Wall. These barracks appeared in the plan of Riga Fortress in 1786. The city of Riga was under the jurisdiction of the Russian Tsar following the Great Northern War between Sweden’s Charles XII and Russia’s Peter the Great. 
Our Lady of Sorrows Church (Sāpju Dievmates baznīca) Is a brick church built in early Classicism form in 1784 to replace the wooden church built in 1761. The facade was altered in the eclectic Byzantine style. The statue of Out Lady of Sorrows that is positioned now to the outside wall of the church had been abandoned by Jesuits in St.Jacobs Cathedral when Gustav II Adolf drove them out of the city. The Lutherans found it among some trash and gave it to the Catholic congregation. 
Statue of St. Christopher ( Lielais Kristaps). The giant standing now is just a copy of the first statue original one stood on the shore of Daugava during the 16th century.. Current statue is on display since 2001, original is stored in Museum of Riga of History and Navigation. The wooden man was considered to be a protector from all evil and especially from floods. Legend about St. Christopher. 
Livu (Livs’) Square ( Livu laukums) it was formed in the middle of the 20th century. On the Square there is located one of the most interesting complexes of residential buildings of 18th century in Riga. In summer time there are a lot of street cafes and life here is never quiet. The most remarkable elements of this Square are residential buildings of the 18th century on Meistaru Street. This is one of the most recognisable “postcard” views of Old Riga. The houses here were attached to the former fortification wall which served as a rear wall of the houses and the houses also shared the lateral walls between them, which allowed considerable savings on materials.
The Cat House ( Kaķu nams) is a building situated in old Riga. It was built in 1909 by architect Friedrich Scheffel. The building is styled as medieval architecture with some elements of Art Nouveau.. It is known for the two cat sculptures with arched backs and raised tails on its roof. It is said that the owner of the house wanted the cats to be placed with their tails turned towards the house of Great Guild, which is nearby, as he held a grudge against its members. It was later ordered that cats should be turned to face the guild house.
Latvian Freedom Monument ( Brīvības piemineklis) is a memorial honouring soldiers killed during the Latvian War of Independence (1918–1920). It is considered an important symbol of the freedom, independence, and sovereignty of Latvia. Unveiled in 1935, the 42-metre (138 ft) high monument of granite, travertine and copper often serves as the focal point of public gatherings and official ceremonies in Riga. The woman at the pinnacle, known simply as the 'Liberty Statue' or affectionately as 'Milda,' holds three stars symbolizing the three regional parts of Latvia: Kurzeme, Vidzeme and Latgale
The National Opera House was constructed in 1863 by the St. Petersburg architect Ludwig Bohnstedt, for the then German-speaking City Theatre, and has been refurbished several times; 1882-1887 (following a fire in 1882), 1957–1958, 1991-1995 (following independence).] A modern annex was added in 2001 with a 300-seat New Hall
Russian Drama Theatre houses the world’s oldest Russian theatre outside of Russia, and the theatre is more than 120 years old, with a rich tradition of acclaimed theatrical performances and celebrity.
The Latvian National Theatre The building was originally designed as the city’s Second Russian Theatre and was designed by A. Reinbergs (1860-1908). It was designed in the so-called Riga Burgher Classical style. The theatre used state-of-the-art technology, and the foyer and stairs were designed in a grand, open style. The statues gracing the entrance were created by sculptor A. Foltz .