It's been a long time since I went to Hawaii but some of my favorites on Oahu were the Bishop Museum, state capital & Pearl Harbor. I had read a book on Hawaiian history, before we went, so I really enjoyed the museum. We got around using the bus, not a rental car. One day, we got on the bus and rode in a circle, meeting many local people who thought we were lost! I agree that you can do many things on the cheap in Hawaii & still see & do a lot. Many years ago, I spent a summer on Oahu & had a great time, even though I didn't have much money. Lucky you to get to spend 5 weeks on all the islands. Have a great time!

On Kauai we went on Liko's power cat out of Waimea for the Napali Coast tour and if the ocean is calm enough they can enter some of the seacaves. If take a boat from the westside you'll pass between Niihau and Kauai and also go by Polihale Beach for some great views.
Highway 340 or the Kahekili highway on Maui has some of the best scenery and we'll probably go on it again in January because nobody took any pics aside from the pulloffs.

Oh, on Oahu, make sure to visit the Doris Duke mansion, Shangri-La. You have to make reservations and the tour starts at the Honolulu Museum of Art where they take you in a bus to the house. Very interesting and somewhat odd place. Get the first tour if you can, as it gets very hot there.

The museum also has some very good exhibits. Plan on hanging around afer the trip in the gift shop (well air-conditioned). The restaurant at the museum is very good and in a very nice courtyard. You MUST have reservations there for lunch, so make those, too.

Marginal, I already sadly learned that the Doris Duke mansion is always closed for the month of September so that's out for me.

I've been to all the islands you mentioned, and here are some opinions:

* Snorkeling -- don't bother with any guided tours. Lots of excellent snorkeling right off the beach, esp on Maui and Big Island, where you can see plenty of sea turtles. On Oahu, Hanauma Bay is the best.

* Summit -- DIY Haleakala on Maui instead of Mauna Kea on BI. You can drive yourself to Haleakala, and hike the Sliding Sands trail -- it's like walking on another planet! Mauna Kea requires a 4WD or going with a tour, and it's not a whole lot better than Haleakala.

* Kayak / Boating -- don't bother the Wailua River on Kauai. Pretty boring. If you really want to go, rent a kayak and go to the Secret Falls yourself--no need to join a tour.

* Na Pali Coast. Splurge on a boat or kayak tour of the Na Pali coast -- the best way to see the Na Pali coast is from the water. We regretted that we didn't do it like this but did a hike and helicopter tour instead.

* Helicopter tour -- we only did in Kauai since many scenic places in Kauai are not accessible by road. But then again, I thought the 1 hour ride was still too short. I think seeing the volcano and lava flow on BI would be cool from the helicopter too.

* Hikes -- again DIY. Favorite hike is the Sliding Sands trail on Haleakala in Maui. I wasn't too impressed by Waimea Canyon -- just a tinier version of the Grand Canyon.

You will love all the islands. I agree w/ Monterey Bob. Nothing will amaze you like a helicopter ride in Kauai. You want to go over Mt. Waialeale. The wettest spot on earth, and hence more waterfalls than you can imagine. Also on all the islands, you won't get a bigger bang for your buck than hiking anywhere. Free, except for the cost of good shoes and mosquito repellent. On Oahu you can hike on Mt. Tantalus and Round top drive just 20 min by bus away from Waikiki. Beautiful view of the urban side of Oahu as well as natural views. On Maui - Hana has a cave tour. I have never been on it, but many people really enjoy it. There are some great horseback rides as well. Skip the ride offered by the hotel and go out to Oheo Stables in Kipahulu. Beautiful hiking near 7 pools as well. Also, near Hana you will find Kahanu Gardens. Not adventure - just astoundingly peaceful, spritual and beautiful. May I ask where you're staying in Hana? You're making me homesick.
Aloha