A couple things to add. On Kauai, as recommended, a helicopter ride that shows you the Na Pali coast will be well worth it; however, I'd also recommend that you do the 2-mile hike into the first beach (Hanakapiai I believe), especially after you've seen it by air. Once there, you can hike another mile or so up the river to the waterfall, even take a dip in the pool there.
On the Big Island, there aren't many beaches, but a really nice one is Hapuna, about 30 minutes north of the airport. I'd also recommend driving to the north shore, going all the way until the road ends--it's a very rustic area, unlike touristy Kona. You can take a little hike down to the beach there as well. Kealakekua Bay is nice visit about 30 minutes south of Kona, and it's where Captain Cook first landed and also was killed (there's a white monument on one end of the bay accessible by boat tour). You should also go to the City of Refuge near there (read up on what it is, interesting stuff). There's a nice restaurant Ray's at the Keahou Sheraton (I believe), and it's name comes from the fact schools of Manta rays feed at night just off the cliffs where the restaurant is located. You can do a boat tour out of Kona for this as well.
Dining options in Kona: my favorite place is "Quinn's almost by the sea." It looks like a dive bar, but has a nice patio in the back, and they buy their fish straight from the boats for the evening's specials. The Brew Pub in Kona is a nice place for a bite too, but it's in an industrial park. Definitely have a cocktail at the Kona Inn and watch the sun set--it's a great setting. If you want a real taste of "local food," try Teshima's about 15-20 minutes south of Kona along the highway. If you're staying in a condo with a kitchen, you can buy fresh ahi at almost any supermarket.
Enjoy.