I have read all the replies, so far, and I think you have received some good advice on hunting the "Big Island". We lived on the Big Island for several years and we enjoyed the hunting the Big Island had to offer: (sheep, goat, wild pigs, turkey, pheasant, chucker,quail and, oh yea......and there's also wild donkeys running around, also....) Lots of sheep and goats on Mauna Kea Mt. and Mauna Loa Mt.
If you are interested in hunting on the Parker Ranch, I might suggest that you go to the Ranch Headquarters in the little town of Kamuela - I'm sure you can find answers there. Also the Dept of Fish and Game, in Hilo, can answer your questions on seasons, hunting areas, license info. etc.
If you want a guided hunt - there's a few 'outfitters' on the Island.
Another little bit of advice......wear 'good' boots. That lava rock is hard on the feet!
Good Luck on the hunt...... Enjoy the Island.