There are plenty B&Bs around Gardiner St., but I can't recommend (or name) any and I wouldn't be keen on them myself-they don't look 'nice'
There is a [broken link removed]on Talbot St, also the Ripley Court, directly accross the road from Busarus and the North Star Hotel within a 2 minute walk. There is also a budget inn (I can't think of the name) of some sort in/around Store St./Busarus.
The Anchor is the first B&B on Gardiner Street on the left. It's run by a friend of mine and I can recommend it. Other alternative is the Jury's Inn on the quay nearby.