Parris Island has been the Marine Corps' main East Coast recruit depot since 1915, and almost every Marine on the east half of the country first learned how to be one here. The museum on base tells that story alongside the longer history of the island, which was a Spanish settlement (Santa Elena) in the sixteenth century before becoming French and then English.
You will need a valid ID to drive on base, but the museum and the surrounding Iwo Jima memorial grounds are open to the public free of charge. If you can time a visit for a Friday morning, the Marine recruit graduation ceremony is also open to civilians and is genuinely impressive.