Both times I've been to Alaska were in June, and the weather was perfect. Pretty much the only thing I've ever done there is rafting though, so early summer was pretty good for that.
Personally my favorite island so far is Oahu (the other one I've been to is Maui). I'm a complete sucker for surfing on Waikiki Beach with all the other amateur surfers :p , watching the insane surfers hit North Shore, and Diamond Head is pretty cool to look at. I loved the snorkeling in Haunama Bay. I'm also a souvenir shop junkie and they have a great outdoor mall with a million and one people selling their goods.
I pretty much only travel in June so I can't attest to the time of year that would be best, but either way you'll have a fabulous trip!
JD
