To back-up the previous posters, the shopping isn't up to much at all. The selection isn't great and the prices are pretty much same as here.
As already mentioned, the beer and food can be very cheap. The SkyBar on the 27th floor of the Hotel Latvia Reval is worth a visit for the view alone, you don't need to be a resident to go there. It's one of the more expensive places for drinks, cocktails are around €5!
If you want to splash out on a restaurant, there's a relaxed Italian called "Fellini" (after the movie director) which is decorated in Fellini-esque, lounge style. The food and sevice is excellent but unlike the rest of Riga, it is expensive. There's also a really trendy bar next to Fellini's called "Light".