My husband and I went to Oahu and Maui with a day trip to Lana'i and a Helicoptor Flight over Moloka'i. I wouldn't recommend planning a vacation to the last two, but they were great for the short time we spent there. I recommend the day trips/helicoptor tours.
Oahu (where Honolulu is) was really nice, but very very touristy. We had a rental car, but we didn't really use it on that island.
For Maui, we needed the rental. The nice places to visit are all sprawled out on Maui. We particularly fell in love with Hana in Maui. What a beautiful, quaint little town, and you definitely need a rental car to get to it...the Hana Highway is a long neverending, crazy, turning stretch of road.
One island that we didn't visit that is increasing in popularity is Kaua'i. If/when we go back to Hawai'i, this will be a stop for us.
I highly recommend the Frommers Hawaii book and the Hawaii for Dummies book. The travel agent we used was Aloha Destinations (McCoy Travel Company). They were great. We have since used them for a trip to Italy.