Opposite Riga's rather grand Hotel Neiburgs is the Hotel Justus. It's not a lot cheaper, but it does have a rather more informal and relaxed feel and it's not a bad place to base yourself if you want to stay in reasonable comfort and meet some nice people. There's a definite wit and irony about the place - the first thing I heard playing through the speakers in reception was "Springtime For Hitler", and it's safe to say you wouldn't get that in many eastern European hotels.
The rooms aren't large, but they're decently decorated and the folk on reception are really, properly helpful - when I mentioned I was thinking about hiring a car, they'd practically got it to the door for me before I changed my mind. Nice bar too. And very good location.