If you are not staying at a hotel in Tybee and are just visiting for the day, I recommend you get a full day parking pass at Parking Lot 2 for $7. It allows you to park at the main parking lot for the beach as well as at any of the parking meters in the city which must be fed at all times.
It is probably better not to park in the main parking lot at the beach as that part of the beach is the most populated. If you drive down a few blocks, and every block has an entrance bridge to the beach, you can find a really nice spot on the beach. These streets all have parking meters so you can park on any of these residential streets and walk right onto the beach.
The parking pass is also great when bar hopping in Tybee as I have already mentioned all streets are paved with parking meters.
The pass does not expire until 12 noon the next day.