Ditto the recommendations for Larry's Music (Sam and his mom and dad are wonderful people) -- the Kapa'a store has a bigger selection but it can be tough to find parking on occasion there.
You also can't miss with the Brick Oven Pizza recommendation -- I like the one in Kalaheo and it is near Scotty's Music for more uke shopping.
My hands down fave spot in Kauai though is the bar at Keoki's Paradise. They have a frozen mai tai that is to die for, it is always my first stop from the airport and often my last stop on the way back to the airport.
Pukadogs are quite good, but if you want a great hamburger, drive up to Anahola for Duane's Ono Charburger. They have a local boy with teriyaki sauce and pineapple that is super yummy. The seating is not great though so I usually get my burger to go and drive down to the nearby beach and eat it there.
If you miss Aldrine at the Waipouli show, I think he performs sometimes by the pool at the Sheraton on Friday nights.
Waimea Canyon is beautiful and you can't go to Kauai without touring the Na Pali coast by boat or helicopter. I've done both and much prefer the boat ride option.
If you have a Costco card, bring it you can get your cheap staples like bottled water there and it is a lot cheaper than ABC stores. If not, there is a Walmart in Lihue where you can stock up on supplies pretty cheap.
And if you like koa wood, you can get some really nice boxes and pieces at the Koa Store - they have a location in Koloa, as well as one near Lihue/Kapa'a. They are a lot cheaper than Martin and Macarthur and you can get nice jewelry boxes, clocks, letter openers, jewelry, etc. from them.
Finally, have a fantastic time. Kauai is my favorite place in all the world. I go as often as I can but still get jealous of anyone who is currently on their way over there.