My wife and I just returned from Kauai on Saturday. We own a time share there and have been to the island 8 times I think. We love it. There is a heck of a lot to do there. Waimea canyon is cool. Barking sands is a great beach (rough drive though and DON'T leave anything in your car). Helicopter tours are very cool, but a bit terrifying for me. I have never hunted there but check out the regs. You can hunt pigs, goat, sheep and blacktail deer I believe. The farmers market at Koloa on Mondays is nice to stock up on veggies for the week. The avocados are unbelievable. We did a kayak trip up the Wailua river up to some falls that was really nice. We have never tubed the ditch but I heard that was really fun. The whole Poipu area is good fun to as is Hanalei. The Costco is just south of Lihue and there is now 2 Safeways on the island for groceries.
As far as food and drink go, the sky's the limit. For a real nice dinner go to the Beach House just west of Poipu and order the Ahi roll appetizer and any fish dish that ends with "in Beur Blanc Sauce". Simply amazing. The Kauai Island Brewing Company in Port Allen is a must. They're food is great and they will can beer for you right at the bar with a canning contraption. It is really cool. On the North end in Hanalei, have lunch at Calypsos and get the fish sandwich, again amazing. For a great pizza, hit the Nawiliwili Tavern by the cruise ship landing. It is really good. Café Portofino at the Marriott right there is pretty good too for Italian.
Have fun, it is a wonderful place to just go and chill out. PM me for any other specifics.