On Kauai there is public transportation, but nothing like on Oahu. The service runs only during the daytime and is the equivilent to shuttle vans or something a bit nicer being used as transport on the main roads. Since the Hyatt Kauai is quite a bit away from the highway, I'm not sure what I would say to do. You might want to rent a bicycle to explore the south shore area. Is there a particular reason you do not want to rent a car? One can be had for fairly reasonable $40 a day or so (maybe even try Priceline!?!) Another option may be to call the hotel and ask for the concierge desk. They are super nice people and there are always two or three of them there to ask any sort of question. (808) 742-1234