Greyfriar's is my favorite coffeehouse in Chattanooga. The coffee is good and cheap (free self-serve refills). The place is usually packed (at least it is in the evenings when I go) and kind of loud. They play a lot of great music (a lot of indie stuff). This coffeehouse is more social than a lot of other places where most people are sitting quietly and reading.
If you have not been to Greyfriar's yet, then I highly recommend that you check it out.