I’ve only been to Grand Cayman once, and it was quite a few years ago. However, it felt much different than other western Caribbean ports. Our experience felt less touristy and more authentic - didn’t have anyone hassling to sell you things, fewer in-your-face tourist traps, etc.
If I recall correctly, we did some sort of island tour excursion which included stops at a sea turtle rescue (very cool), Hell, Seven Mile Beach, a rum distillery, and drove around the island giving some history. We also walked around the downtown George Town area and are some authentic local food at a food stall - turtle soup and conch fritters. It was awesome! We really want to make it back at some point. I’m sorry I don’t have more details or suggestions (it was just one call over five years ago after all), but we all look back on that call fondly and agree that Grand Cayman is our favorite port in the Western Caribbean.
Also love New Braunfels - we have lived here for generations and remember when it was just another small dot on the map… not anymore! LOL