We booked a snorkeling boat trip with White Sands while on the island last month. We called the day before we wanted to go, and booked an afternoon 2-stop snorkel trip on a motor boat (they offer sailboat and jet ski snorkel trips too). It's the off season, and we ended up being the only two people who booked for that trip. Most operations on the island would cancel a trip with only two reservations, but White Sands was happy to accommodate, and said they wouldn't think of canceling given we drove across the island from our Seven Mile Beach hotel to take the trip. So, we got an unexpected private snorkel boat tour, which was awesome! (Given that the max number of guests on a trip is six, I think everyone would get lots of individual attention even on a full trip.)
Dave was our guide, and he did a great job. He took us out to the two different snorkel locations, which were both fabulous and far more vibrant than what we saw on the west side of the island. WAY more fish and healthier reefs than the west side of the island. Saw several dozen species of fish, sharks, rays, vibrant coral heads with huge sea fans, and lots of other snorkeling awesomeness.
We were the only boat at the first stop (there are not a lot of snorkel operations on the east end, so the stops are way less crowded) and upon arriving at the second stop, Dave saw that the other boat was getting ready to leave, so we took a short detour to a shipwreck so that we could have the second stop to ourselves too. Dave was super helpful at helping us identify the fish we were seeing. Dave also filled us in on lots of history, things to do and places to eat on the island.
If you're going to go all the way to the Cayman Islands, definitely make the extra effort to drive over to the other side of the island and take a snorkel trip with White Sands. It's the best snorkeling I've ever done, and the hospitality was fantastic. We definitely felt we were getting off the beaten path and having a more authentic (and less crowded) Cayman experience than was available on the west side of the island. I think it would be great with kids as long as the kids are comfortable in the water - the sites had really calm water and even the deeper of the two sites was only 15-20' with really tall reefs so lots to see just under the surface. It was the highlight of a great day exploring the quieter parts of the island.