Have just returned from a week in Riga. I was rather nervous about going to Riga after having read reports of people being ripped-off and mugged, but I have to say i need not have been. We stayed in a nice cheap apartment right in the old town and so had plenty to do day and night.We took the train to Jurmala, visited the zoo and did alot of walking around the historical sights.
We did not encounter any problems, although we did notice that shop assistants were a little grumpy. First we thought it was because we couldnt speak the language, then realised they were the same with the locals! We had no problems in restaurants and bars and were never charged above the menu price.
The lady that took us to the aprtment was very pleasant and even negotiated a lower price on the apartment before we got there.
We were approached in the street, also by a young woman claiming to have no money and needed to get a train ticket, but that type of scam happens in many cities. So i would say do not worry if you blend in with the locals, everything should be fine.