Riga is a very versatile town for the heritage enthusiast. The Historic Centre of Riga has several interesting parts.
The old town centre of this member of the Hanseatic league with its cobbled streets, the Riga cathedral with a beautiful closed cloister with remains of the old town. St Peter Church with the original Roland Statue and the elevator to take you up the tower for a wonderful view. The square with the painstakingly rebuild House of the Blackheads and also to mention the museum of the occupation of Latvia, this museum will give you an insight of the more recent history. Smaller but must see locations are the three brothers (three old houses), Riga Castle, the swedish gate and the small guild (do go insight, it is not very well known but a little gem, see the photos).
Then of course Riga has the highest concentration of Art Nouveau buildings in the world. Just walk along the streets and enjoy these outstanding buildings in Art Nouveau / Jugundstil style. This really must be unparalleled in the world. One of the great architects of these buildings is Mikhael Eisenstein (his son was the famous movie director Sergey Eisenstein (Pantzerkreuzer Potemkin)). Look at the plaster sculptures with faces, animals, creatures etc.
The Academy of Science is housed in a skyscraper in Sovjet style. There is a wonderful viewing platform high up the building (elevator!). The skyscraper was build in the fifties and was paid for by the Kolkhozez in Latvia. See the decoration with the hammers and sickles as well as the Latvian folk ornaments and motifs.
Down by the skyscraper you will find the old market housed in buildings used to house zeppelins from Germany.
Take a look up the freedom monument at do visit the orthodox church with its golden roof.
Riga in Latvia is a very versatile town indeed. Although not a part of the World Heritage Site it is worth the trip to go to Jurmala, the beach resort of Riga.