Hi there. I lived in Hawaii for 13 years (Oahu, Maui & now Big Island) and am an avid tourer so I hope I can help some. Unfortunately, there are some real problems about getting your bike here. The airlines have weirded out since 9-11. On interisland flights, you used to be able to just roll your bike up w/ handlebars turned and they would take 'em generally with no charge. However, just 2 weeks ago, I flew from Las Vegas to home (Big Island) on Hawaiian and they almost refused my bike in a Trico IronCase because they said they thought it was too big, then it weighed too much, then they wanted to charge me $75!! And this was the week of the Ironman!!! Yikes! I ended up repacking the case and after arguing I paid $50. If you are insistent on biking Hawaii, I would check out what www.sportsexpress.com
can do for you FedExing your bike from island to island. It might be cheaper. Also check with the airlines - Aloha & Hawaiian and get their costs IN WRITING.
Once you get to Hawaii, the riding is very good. Oahu has the big city of Honolulu & Waikiki and it is a pretty scary place to ride. But once you get out toward North Shore or the Windward or Leeward sides, things calm down a bit. Still, I wouldn't really make Oahu a bicycle touring destination. Once nice thing is that The Bus does have bicycle carriers and you can get anywhere on Oahu on it. Camping options on Oahu are very limited.
Maui is a much more friendly island to bike but again camping options are not particularly plentiful. Lanai and Molokai islands are both accessible by ferry from Maui. These two islands are very sleepy and I think would make pleasing destinations. Lanai has a campground right where the ferry lands. I am uncertain of camping options on Molokai. I have wanted to tour to Molokai but I think I would go on my MTB not my touring bike. I think Kauai would also be a great destination.
Big Island offers the best bicycling in the entire state. In fact I live on the best asphalt in the state. I picked where I live now for its good bicycling. There are an adequate number of camping facilities almost perfectly distributed along the perimeter of the island. 2 years ago, I did a wonderful 10 day, 500 mile tour around and across the Big Island. So, I would encourage you to come to Big Island; there are many things to see and do that are likely to be completely different from many other destinations. But, just don't expect mainland-style camping facilities. Unfortuantely, I think most folks here think that camping is for homeless people. Camping here is pretty embarassing but although facilities may be pretty trashy I have never felt threatened (but be smart). It is still pretty third world so bring your water filter as potable water is often difficult to come by.
Campgrounds on all islands are either managed by the respective County for each island (Oahu is Honolulu County), State or National Parks system. You can get a lot of information about camping options on the internet.
With all this said, let me refer you to 3 books: Hawaii by Bike by Nadine Slavinski; Cycling Hawaii by Jeff Baldwin and Camping Hawaii by Richard McMahon. These are a little old and not always accurate but at least they will get you started.
Please feel free to contact me for any additional information. I would love to help.
Roberta in Hawaii