You can fish anywhere there in the state where the shoreline is not restricted. South Point on the Big Island and Kamaole Beach Park on Maui are popular locations. Freshwater anglers will find plenty of angling opportunities in Hawaii's Wailua and Nu'uanu Reservoirs, as well as Wahiawa Public Fishing Area and Koke'e State Park. Bottom and reef fishing is often restricted due to overfishing, so check for the most up to date regulations on Department Aquatic Resources website.
Check out these Wheeler Army Airfield, HI fishing resources:
