Feel free to email me for more details and specifics. I've lived and hiked in Hawaii for 2 years now, and this year i'll be living there half-time.
Time of year: anytime. September and October can be hot. December-March can be cooler and much rainier, but there are no guarantees. It's the tropics...rain happens. Occasionally Mauna Kea can be closed by a snowstorm for a few days in January or February, but generally any time of year is a good time of year to be in Hawaii. If it rains, you get in the car and drive around the island to the side where it is NOT raining.
Lodging: it may be one place where you'll still do well by a travel agent. Package deals can be cheaper through them. If you're interested in a basic condo on Oahu far away from Waikiki, i might have a reference. If you want someplace very nice, expect it to be pricey.
Rental cars: try Thrifty, or packages through an agent. Don't sweat the waivers saying you can't take rental cars up Mauna Kea. Everyone does it. The road is perfectly fine. Just don't run out of gas or anything, or you'll eat the towing cost.
Inter-island flights: Some new airlines are causing some great cheap competitive rates. Try Island Air, or google "hawaii new airlines."
Guidebooks: Wizard publications has a series of bright blue guidebooks called things like "Big Island Revealed" and "Hidden Oahu," etc. They are the best. I don't always agree with their restaurant reviews, but they are excellent on directions and ideas for fantastic places off the beaten path, including hikes. On Oahu, the hiking book by Stuart Ball is sort of the bible for the topic.
On the Big Island, plan at least a full day and night for Kilauea. (the active volcano.)
On Maui, the climb up to Haleakala via Kaupo Gap is strenuous, logistically difficult (in terms of spotting cars), but fantastic. The road to Hana is touristy but wonderful. Plan TWO days for that, and camp at Waianapanapa. Check the guidebook above for the "Blue Pool."
On Oahu, the hike options are endless and not easy. The experience of wading out to an island at Maleakahana is memorable. The drive or hike up Tantalus is must-do. The snorkeling at Hanauma Bay is worth dealing with the crowds. One needn't be much of a swimmer there to see a gazillion fish.
On Kauai, the Kalalau trail needs at least 3 days to be worth it, but right now ranks as one of my top 3 hiking experiences ever.