Best time to go to Hawaii is whenever you have time off. But my favorite time is June-July: mangoees, lychees, and many others, plus not so many tourists, and usually lots of good events going on.
In summer months there are some artocarpus like jackfruits and chempedaks.
Best island for fruits is island of Hawaii, and best side is Hilo side.
If you do a search this same question has been asked many times and places to visit have been listed.