Wherever you go in the islands, there is fantastic stuff to see and do. My husband and I go almost every year, and here's a quick overview of what we would consider "musts". Feel free to PM me for more info, website links, etc. I'm kind of a frustrated travel agent and am happy to talk about this kind of stuff in detail!
In no particular order...
Oahu - North Shore/Haleiwa for the surf (even just to watch it), the Pali Lookout (as Wahine Ina said), beautiful Lanikai Beach, Haumana Bay, the Polynesian Cultural Center for a day's worth of photo ops and learning about traditional Hawaii and beyond. For food/drinks, La Mariana is an absolute must-do old-school tiki palace. Also maybe consider checking out some of the grand hotels/bars along Waikiki - the Moana Surfrider, Royal Hawaiian Hotel, Halekulani, etc. Byodo-in Temple, Iolani Palace, and the Bishop Museum if you're into history/culture.
The Big Island - Rugbymatt's right; stay on the Kona side. It's sunnier and there's lots to do. Drive up around the crater at Kilauea! Awesome. Place of Refuge for history and tikis and snorkeling at Kealakekua Bay. We haven't done it yet but are planning to later in the year - a road trip to the gorgeous Hamaukua coast and Waipio. Maybe do the sunset/stargazing trip up to Mauna Kea (another one we haven't done, but are planning). Dinner at Don the Beachcombers, with drinks at their Mai Tai bar at sunset - you might get lucky and see the green flash!
Maui - We love the Ka'anapali area to stay in - close to Lahaina Town and one of the most beautiful beaches in the world, I think. Also you can snorkel right off the beach at Black Rock and see turtles. Drive the Hana Highway. Go upcountry to the cowboy town of Makawao and on up the Haleakala volcano to the top. There are a ton of scenic drives - I'ao Valley, West Maui mountains, Hana Highway, etc. If you can afford it, eat at Mama's Fish House in Paia - expensive but the "upscale tiki" vibe and the amazing food are worth the splurge.
If you think you might be going to Kaua'i, I have info for that, too - just let me know.
I can keep going, but that'll do for now. You'll have a great time, I'm sure!