I'm sure a jeep/4x4 would be fun, but there's no need for one, on Oahu anywhere, and on most parts of Maui.

On Oahu, I'd recommend you look at renting in the Kailua/Lanikai beach area, or on the North Shore. Anything in the Honolulu/Waikiki areas, basically from Waikiki to Kapolei will not be a "quiet area".

Check out VRBO for the North Shore/Haliewa/Waimea area - and also - the Turtle Bay Inn has cottages away from the main buildings. We also enjoyed staying at a nice B & B over by beautiful Laniki Beach.

There is no problem getting to Hana in a rental car and a 4x4 is not necessary. Your time their will be very peaceful and quiet and there are many coastal areas nearby that are stunningly beautiful. The book Maui Revealed does an outstanding job of telling you how to get to all the best sites, hikes, beaches and waterfalls on the way to as well as in and around Hana. The other quiet areas of Maui are along the Up Country road that goes to the top of Haleakela Crater and the coastal road that goes northeast of Kapalua.
On Oahu, you will see the most quiet and beautiful areas by driving the coastal road around the island starting out going east from Honolulu and Waikiki. It will take 40 minutes to escape the urban and suburban environments but then it will be beautiful from that point on. A good guide book will help you find all the scenic sights along the drive.
Have fun.

Thanks for the suggestions, and I've ordered the book on Maui. Still a bit in awe of where to go while in Oahu but getting some good ideas!
Wherever we end up I'm sure it will be a great trip.
thanks.

Driving on Oahu is not really all that complicated, even though Honolulu is a city.

From Honolulu/Waikiki Beach - If you drive 20 minutes "south" (note - the original Hawaiians used the next point of land when referring to directions ) - on H1 - you pass by Hawaii Kai and up the hill to the turnoff for beautiful Hanauma Bay -
http://www1.honolulu.gov/parks/facility/hanaumabay/information.htm

Beyond that - there is Sea World and very little population - even in Waimanalo (where they filmed much of Magnum PI with Tom Selleck way back when) - until you reach Kailua - mid-island or so on the east side. http://www.aloha-hawaii.com/oahu/kailua/

If you headed north - in 25 minutes or so - H1 to H2 - about the center of the island - you pass by Wahiwa/Schoefield Barracks http://en.wikipedia.org/wiki/Schofield_Barracks and then it's pineapple fields all the way to the beautiful North Shore - through Haleiwa and then past the fabled Pipeline/Sunset beaches to Turtle Bay resort and the like.

And if you head "east" - H3 - through the Koolahu's - via the Pali tunnel (see the Kailua pic above) - you can stop at the magnificent Pali Lookout (in about 20 minutes) and then continue down in Kailua and either North toward the Polynesian Culture Center and Turtle Bay - or swing south to come back around to Hono - past Hanauma Bay.

Here is a driving map of Oahu. http://www.aaccessmaps.com/show/map/us/hi/oahu

Actually - it's called Sea Life Park (we have Sea World here in SD) - and even if you don't swim with Dolphins, if you are there when the diver feeds the fish in the tank - that's fun to see. http://www.sealifeparkhawaii.com/

And for Pearl Harbor - only the "Navy Boats" actually let you get on the USS Arizona/Memorial. Suggest you arrive early to beat the crowds - and you might also be able to make reservations.

see: http://www.pearlharboroahu.com/?gclid=CKn_87mEm68CFaYZQgodMDC-bg