bars with music in village
I give a strong vote to Knickerbocker Bar & Grill, located at 33 University Place (corner of 9th Street). Knickerbocker's is nominally a steakhouse (and I think their steaks are worth ordering), but it has a full and varied menu, with a good winelist. The seating is comfortable, and they have jazz combos that start around 9:00 PM. There is a music charge once the music starts, but I don't think it's outrageous.
I've always thought Knickerbocker's is very much underrated. Only problem I've ever had with them is that it gets pretty crowded, so I'd recommend reservations (although the lady who handles the reservations has a bit of an attitude, not so much on the phone as honoring them when you arrive).
In my experience, once you are seated the service couldn't be friendlier, and they don't try to rush you out.
I ate some pasta at Cornelia St. Cafe that was acceptable, even rather tasty (I was hungry at the time, however). But if I were you (which I'm not, so take this with a grain of salt), I'd be at least as interested in the quality of the group(s) playing as the food, however. Let me rephrase that: There are a lot of good places you could eat at in the Village BEFORE going to a bar and hearing some nice jazz over a couple of drinks. YMMV