- Crazy Elephant @ Clarke Quay is a good place to start. They play mainly rock blues.
- Roomful Of Blues @ Prinsep St has pics of blues legends hanging on all their walls. On the weekdays, Gilbert plays as a one man band. He doesn't concentrate on just blues though. It's pretty varied from the evergreens to stuffs from the 60's & 70's.
- There's also a pub called Jazz @ Southbridge which may be of interest to you.