I usually go for specific sets that I'm interested in, rather than just hitting a spot. If I am going to just hear someone play, I tend to go to Fat Cat which is in the village–$3 cover, music every night but can get a bit hectic on weekends since it's right near NYU. I've got a friend who swears by Tomi Jazz, also in the city, but I've yet to go.
I think the Brooklyn venue I've been to the most in the past year or two has been National Sawdust. It's a bit pricey and not really the vibe I'd shoot for 24/7 but they have some really excellent concerts.
Hopefully I can come out for the next BCC show!