Definitely second BillM's recommendation of going to see Doug & Sandy McMaster up in Hanalei! Awesome small show and stories. They also hang around afterward and are very helpful with any info you might need. Genuinely nice people!
Larry's Chicken In A Barrel in Kapa'a. Also Kauai Music & Sound is a great music store to explore - Dave Greenberg is a great person to deal with (no pressure, let you try anything you'd like, willing to answer any questions).
I think that Aldrine & Aaron from UU play at the Oasis Bar in Kapa'a on Wednesday nights.
Rent a Jeep at the airport - some of the better beaches are easier to access with one (and if your Hyundai sedan rental gets stuck in the sand, you'll be out a lot of money!!). Saw some nitwits on one of the clearly marked "4WD only" roads with their rental convertible dug in up to the rocker panels....
Poipu Beach Park is really good for snorkeling and seeing the occasional honu or monk seal sunning itself on the beach
I would also recommend the Kayak/hiking tour with Wailua River Guides, we went on a helicopter ride with Blue Hawaiian, and I think we went with Holo-Holo Tours on a sail along the Nepali coast
When I was there, I stayed at the Aston Islander On the Beach (
http://www.astonislander.com/)