I used to live in Riga.
I'd mostly stick to the Old Town. Kiwi bar was the place to drink then. If the weather is nice there are loads of little bars with seating on the street - just settle in and people watch, Dome square comes to mind. Latvians come across as unfriendly and rude, just try to let it slide, mostly they don't mean it, its just the way they are. Also, if its still there, there is an Indian resturant next to the Kiwi bar - it does a fantastic curry.
Also, if a couple of very pretty girls start drinking with you and then suggest you come to a club with them - don't go, most likely you'll be presented with an eyewatering bill at the end of the night. To be fair, I don't think that sort of thing happens so much anymore. As I understand it, most of the real sleazy places have been shutdown or pushed out of the center.
Riga is mostly safe, certainly more so than London, nonetheless when things get violent they can get extremely violent. So be careful. Respect the Police, they're not adverse to giving you a battering if you're drunk and out of control. And again, to be fair, this sort of stuff does'nt happen so much anymore.