If you've never been to GC, Stingray city is a must.
As a crew member, a great day without too much hassle or money spent is to go to the Governor's House Beach. You simply get off the tender, pick up a sandwich at subway, and hop in a local bus to the governor's house. Hardly any tourists get dropped off there because there is no restaurants or facilities.
The beach is beautiful and usually not too many people on the beach there.