The Rhythm Room is an excellent venue (though I'm non too fond of the ownership). Highly recommended.
A not as good acoustics club, but my favorite R&B venue is a little west of the RR, is Chars. Very down home, people know their music, and a bit more local flavor. I always loved playing there.
The rest is kind of hit and miss with different acts all over the place, but nowhere in particular being dependable. You can find surprisingly good acts, even in duos and trios in the restaurants or not so much. The Phoenix New Times is another resource.
Phoenix Music - Phoenix Concerts and Clubs
