We've been on a Bahamas kick recently. 3 hour flight there and 2 hour 50 minute flight back direct from IAH. Check out Baha Mar - one of the 3 hotels will probably work for most budgets and desired amenities. It's only about 20 minutes from the airport, so you don't waste a lot of timing traveling post arrival which helps for a short trip. Tons of restaurants for dinners and plenty to do on site (tons of pools, huge beach area, big casino, crap load of restaurants, and plenty of options of off site as well that depart from their pier. Rosewood is more expensive but also feels a LOT more secluded if that is valuable for you - their private pool area is really quiet and their section of the beach is way less busy. If you aren't interested in that, the Hyatt should be just fine and you have access to all of the same amenities other than the private pool and beach area along with a much smaller room bill!
Only potential issue is I think the latest direct departure time from IAH is noon which might not fit into your Thursday PM target. With a short trip, I think you'd definitely want to arrive on Thursday so you get two full days before leaving Sunday afternoon (latest departure is around 5PM).
https://bahamar.com/Haven't been to Cayman in a while but I think it would be pretty tough to go wrong there as well, especially if you primarily want to hang out on the beach.
