Vehicles have the right of way, they are not required to stop for bikes. Stop at all crossings. Use of the roads, where bike paths exist, is prohibited.
Be considerate of walkers and joggers on the path. Warn them of your approach by saying "passing on your left".
Important - If you leave Sea Pines through either gate, be sure to take a picture of the entry code. Upon your return, you will need this code to get back in to Sea Pines. Otherwise, you will need to bike back on the beach.
Stay off the golf cart paths unless otherwise posted.
There are numerous bike rental companies on the island. Just do a Google search for "bike rentals on Hilton Head". Most of them will deliver and pick-up.
South Beach Bicycle Rentals is right next door and is a good bet in case you need any fine tuning on your rental.