I will have a Thursday-to-Sunday there with ds, soon.
The one must on our list is the open air pool. We love it!
On past visits we enjoyed Beaulieu and Hurst Castle. Fort Victoria on the IoW was also good, Alum Bay so-so.
Where else should we go? We will have a car, but don't want to 'waste' time travelling. Unless, of course, part of the travel is fun (eg the ferry) or can be fitted into the way there or back.