I was there last February for 3 days with 8 other girls and we stayed in Hotel Riga which was a perfect location in the middle of the city just off the main square, and not expensive. We had a great time, the irish bar we were in wasn't great but the local bars were great fun.
Food (and local beer) was lovely and cheap (compared to here!). There was a bit of sightseeing but not a huge amount, I'd say 3 days would be plenty, and there was a lovely open air ice skating rink which was only 75c per hour !!