The mugs are usually available in your room (there were 6 mugs in our studio two weeks ago). The cost is $10.99/mug, and it is added to your bill after check out. You can refill your mug at Hurricane Hannah's (SAB), Beaches 'n Creme, and the Breakfast Bar next to Cape May Cafe. HTH!
We ate breakfast at Yacht Club Galley one day and they filled ours with iced tea because it was before 11 a.m. and B&C and Hurricane Hannah's weren't open yet.