For introduction I give here the 10 most popular "things to do in Riga" from tripadvisor.com:
10 - Riga Zoo
9 - Central market
8 - Riga castle
7 - Dome cathedral
6 - House of blackheads
5 - Freedom monument
4 - St. Peters Church
3 - Brother`s cemetary
2 - The museum of occupation of Latvia
1 - Old city
Personally I find this list (although it is made by popular vote) a bit too predictable - all these are textbook tourist attractions that don`t really say anything about our city. What would I suggest?
1) Visit Riga Old town - I would love to be original and ommit it but it is the main attraction of Riga anyhow. But I could suggest you choosing the narrower and less populated streets of Old Riga because those have a more authentic feeling (by walking through Old Riga you`ll surely also see the Dome cathedral and the St.Peters church, so technically those aren`t really separate attraction objects)
2) Play a game of chess in do it. and why not?
3) Take a ride on the retro-tram
4) Take a walk through Maskavas forštate (preferrably - not alone and not after dark)
5) Feed bread to ducks in the Riga city canal (or in Arkādijas park)
6) To keep up with the cultural part - visit Alberta street to see some nice Art Noveau buildings
7) Have lunch at Lido. It`s not an advert from my side, it`s just a thing you must to in Riga.
8) Go on a tour in the Laima chocolate factory
9) Have a beer in a beer garden in Old Riga (but make sure you`re drinking real beer and not some bottled beer-imitation. Choose Tervetes, Bauskas, Užavas or Piebalgas beer. Never try Aldaris)
10) Go up the Riga television tower and have a look at the city.
At the moment I`m too lazy to make a similar list for Latvia but eventually I`ll make one at some point of time. If you have any additions, corrections, updates or anything else for my list - you`re welcome to express you opinion. Even if it is absolutely nothing like mine and you want to call me a barbaric troglodyte.