Since we only visited the lighthouse, we were able to park in the lighthouse parking lot for free. It apparently is unusual to be able to park on Tybee without feeding a meter. If you can find an old film can, they hold a couple of dollars worth of quarters. (That's also the way I take my quarters for the laundromat)
The lighthouse website says:
CAR PARKING: Parking is free next to the Lighthouse.
COACH AND BUS PARKING: You can not park next to the Lighthouse. You can drive through the circle drive at the Museum and get wrist bands. The City will allow coach and bus parking in the North Beach Parking lot. It is required that you turn the motor off whilst parked. Look for the "North Beach Parking" signs. For more information call Tybee Island Parking Services. Charges may be as high as $8 per bus or coach.
There is NO taxi service on Tybee so make sure you plan ahead if you plan on going out drinking and think you might end up drinking too much..They do Rent bicycles though at a few places there so that is an option..I think they have some sort of shuttle bus come there from out of Savannah though.