I spent about five days in Riga last month with my girlfriend. Be sure to get the book
Another Travel Guide Riga. Excellent with lots of interesting places you'd never see in a standard tourist guide. Each thing gets it own page (or two!) - not the usual endless lists of everything in every category - AND it's printed on high-quality paper and features nice photography.
Really, just get the book (from amazon.co.uk or in Riga) - it's really worth it - everything I'd recommend is in there...: Istaba (nice shop and GREAT restaurant), Meta-Kafe (good coffee [for Riga], brilliant & cheap breakfast/brunch, interesting books, good music..), Latgalite market (ask before taking pictures!), going up in "Stalin's birthday cake", etc... wandering around in some rougher areas was certainly interesting.
There's also a a
free "alternative" tour every day, but as is turned out we had already been to most of what they showed (thanks to the aforementioned book), so not really worth it.
For general information, download the pdf of
Riga in your pocket (also available for free at the airport and elsewhere).