Welcome to the message board. Sorry to break the bad news to you but there's no where to go kart here in Grand Cayman. Believe it or not there used to be only one place you could do this and it was in a guys basement. Yeah his house was so big that the lowest floor he used to have a track and race around. Obviously you'd have to be friends with the guy it wasn't a commercial thing. Anyways that doesn't even exist anymore from what I understand. As far as miniature golf once again am sorry to disappoint. There used to be Cayman Crazy Golf but it's closed and I'm not sure if it will ever open again. It's still there but not operating.
Other things you might like you check out and try doing. There's a place called Kings Sports Center on Crewe Road where you can go staking (well roller blading) around a rink. They also have a climbing wall. If I were you I'd consider doing that but also you may like to check out some of the many other things Cayman has to offer. For example Stingray City, Starfish Point, Crystal Cave and especially the Turtle Center are all great things to do as families with kids. Honestly if you do some google searches or check out Trip Advisor you'll find a ton of activities.
