Anna Maria Island (one island north from Longboat Key) is a great place to go for a catamaran-sailing vacation. I know many beaches where you can keep your cat for free, and there are a lot of beach rentals that would allow you to keep the boat right out the back door!

If you want to stay at a Hotel, I know of one with a catamaran / watercraft rental operation on the beach across the street from it. You could rent those, or keep your own on that beach. You could also keep it on a beach a short drive from wherever you decide to stay.

There are many nice water-front restaurants that you can sail up to, or you could sail off to Egmont Key (no road access) and explore WWII ruins and brick roads winding aimlessly around what used to be a bustling military installation.