In addition to the other suggestions, The Sandbar in the (former Caravanseri), now Morgan Complex, has different kinds of music on different nights. I confess I don't know which nights they have what kinds of music. There is also Karakter. They also have music a couple nights a week.

Also, regarding Fat Tony's, I love the music there, but the restaurant is way too crowded for me on Tuesday nights. However, there are several other restaurants in that area, including Spaghetti House, where you can sit outside and enjoy the music from Fat Tony's.