Man, I was there for 3 months for work but came home just prior to Christmas. I toured the stadium (since I stayed about 2 blocks away) and was wishing it was February and not December. Anyhow, if you're a newbie to Hawaii, I recommend Huanama Bay for a bit of snorkeling. It's about a 15 minute drive east on HI 1 and costs like 5 bucks (unless you're in the military). There are always sea turtles and tons of fish. Waikiki is OK, but there are many other beaches to see like Turtle Bay on the North Shore. And don't miss the Pearl Harbor stuff. In fact, while you're on the battleship you can look across the bay and probably see a number of foreign vessels. A good buddy of mine is the ship project officer for the Japanese destroyer Atago (for another 3-4 weeks) which should be directly across from the battleship. Oh.... and you gotta try the Spam and rice from McDonalds. It's pretty funny seeing the odd menu items and is worth a try. The Diamondhead hike is about 5 miles east of the stadium (along the beach) and is a fairly good workout, and the view is pretty awesome.
For souveniers - the ABC stores got just about everything you need. But as you're heading downtown (from the airport) there's Hilo Hatties on Nimits Blvd pretty close to the industrial piers. It's got EVERYTHING you could want to bring home and they offer decent discounts. Further down Nimitz there is a Goodwill and/or a Salvation Army if you're looking for an aloha shirt for cheap (new ones run anywhere from $15-$80). Then, of course there is a butt-ton of malls and such as you get down near Waikiki (past downtown Honolulu). A good pit stop is the Hooters at the Aloha Towers. If you see the big "Superferry" near downtown Honolulu find a parking spot and head to the water, Hooters is in a little strip mall at the base of the Aloha Tower.
If you reverse course on Nimitz (heading west from the airport) you'll hit the Harley store and a couple of good eateries).
Ummm.... that's all I can think of for now. Post any questions and I'll get back to you ASAP! I'm green with envy.......