Though renting a car is encouraged, there are public transit busing options for getting around Hawaii.
Honolulu (Oahu): TheBus
Kahului (Maui): Maui Bus
Kona (Island of Hawaii): Hele-On Bus
Hilo (Island of Hawaii): Hele-On Bus
Lihue (Kauai): Kauai Bus
Rideshare services are available, but securing a ride may be difficult outside of normal business hours. Reserving a ride in advance is highly recommended.