You can't rent the house on the island but there are guided overnight trips that you can sign up for through Coastal Expeditions. They are very popular and require planning/booking at least a year in advance. If you want to stay nearby and do a day trip to the island your best bet is to look for a hotel in north Mount Pleasant or maybe Georgetown. The landing that you meet at to take the ferry boat over to the island is in Awendaw but I don't think there are any hotels in Awendaw.
No, but I believe you can still rent the house on Bulls Island for a couple of days.
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