I'm lining up a few days in Honolulu next month. While there are things on that island that I want to see (Pearl Harbour etc), I'd really love to get to Mauna Kea as well.
Wikitravel's Honololu article doesn't really explain much about getting to other islands, however.
What's the easiest and cheapest backpacker-style way to change islands. I assume helicopters are options, but there must be a cheaper way?
Pearl Harbor might be a little easier to get to when in Honolulu. There are regularly scheduled buses that go to Pearl Harbor. The ones you are looking for are Route 9, PH2, PH3, PH4, PH5. There is one free transfer with any one way fare and fare for an adult is $2.50 one way.
The best I could find on Mauna Kea is the organized tour which will run about $200 but you will need to fly from Honolulu to Kona or Hilo on the Big Island to take advantage of it and that will be another $200 plus depending on how few days you are actually in Hawaii it may not even be feasible.
EDIT
Found this link talking about ferry services on the Islands
