I too would recommend Rum Point. We rented a car (
avis) through
www.grandcaymancruiseexcursions.com. Pickup is by shuttle at the blue iguana at the pier. About a 10 minute ride over to the airport location. We were last off the minivan so last in line to get our cheap car ($43 including insurance and gas). Lucky us. Ahh, but 10 minutes later when they got to us, everyone else took all the cheap cars, so we got a free upgrade to a black jeep! Woohoo! We drove the long way around the island past the blowholes, to the wreck of 10 sails (you can actually see the ship laying out there!) and some awesome mansions/homes on the east side. We got to Rum Point around 10am, so I don't think it took too long overall.
We pre-booked a stingray snorkel through red sail sports that started around 11:15. Good thing is rum point is closer to stingray sandbar so it only takes 15 minutes by boat. Yes, its true you can see the ships across the bay. When we were on our stingray snorkel trip, an elderly couple said, "boy look at all those cruise ships. Sure glad we are on this side of the island away from all those people" Then, they asked where we were staying. Alas, we had to tell them "on the cruise ship"!!! ha ha.
We didn't eat at Rum Point, but the outdoor cafes smelled wonderful with fresh fish a grilling! We had brought our collapsible cooler with some sandwiches and water from the ship. You can't actually eat them at Rum Point though...for that we had to walk back to the car, which is very close to the beach anyway. Some nice shops. No chair hogs at all! A great location to get away from all of the hubub of the other passengers. We took the short way back (about 30 minutes) cutting across the island and still had plenty of time to shop in town before reboarding the ship.
I would definitely recommend a visit to Rum Point!