Sullivan's Island is small on purpose and intends to stay that way. Middle Street is the commercial stretch, the beach accesses run by station number, and there's no rental counter anywhere on the island.
That last part matters if you're staying out there. Anybody who needs a car is driving off the island to get one.
The shape of a day
Fort Moultrie sits at the west end near Breach Inlet with the lighthouse on the same stretch. The beach accesses run east from there by station. Middle Street handles lunch and dinner, and it's walkable once you have parked, which is the catch.
Parking is street parking and it's tight in season. This is one of the few places where a smaller car is genuinely the better rental. The Fiat 500X fits near the stations in a way a full-size SUV does not.
Pairing it with Isle of Palms
Breach Inlet separates Sullivan's from Isle of Palms, and most visitors treat the two as one trip. If your group is bigger or you're carrying beach gear for the day, the SUV makes more sense and you accept the parking trade.
Getting the car
Pickup is at 1471 Folly Road on James Island, about 30 minutes out: over the Ravenel, through Mount Pleasant, then the Ben Sawyer Bridge onto the island. Book online from the booking page, and the Sullivan's Island page has the rest of the detail.