If you only plan to spend one day off the resort, I might suggest that you simply take a taxi ride to the heart of 7 Mile Beach (Sun beach is a good place to start) and walk the beach. The experience that you will get walking the public beach is vastly different than the one you will get on the resort. It's understandable that you paid for all-inclusive and that you want to get your money's worth, so if you only have time for one "excursion" I wouldn't discount a day on the beach. You can stop at the various bars/restaurants, take in some live music, browse the vendors and maybe jump on a glass bottom boat ride. This is an excursion that will cost you only what you are willing to spend at the various venues.
Aside from the beach, I would also suggest the One Love Pub Crawl on the West End. This will only cost you a tip to the driver and whatever you spend drinking at each bar.
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