East Kent is quite a deprived part of the UK, but is really interesting in a lot of ways. I'm sure others will pile in with all the things I've missed.
Richborough Castle near Sandwich. It was closed to have work done, not sure if it's re-opened.
The Maritime Museum, Ramsgate Harbour. Run by volunteers, so don't expect fancy high tech exhibits, but there is a lot to see, all about Ramsgate maritime history, including both World Wars. There are sometimes a couple of the Little Ships in Ramsgate Harbour too. Some nice little bars and cafes under the arches along the harbour front.
Deal has a little maritime museum too.
Margate has caves to visit as well as the shell grotto.
East Kent once had coal mines, and there is a mining museum, but I've never been there, so don't know whether it's worth visiting.
And there is some lovely countryside with ancient churches and old buildings, just to drive through, or take a bus ride through.
Near to Chatham Dockyard, the Royal Engineers Museum. Both require more than a full day, so you can't do them in one day. And the (free) Guildhall Museum in Rochester, especially the hulks exhibition. There's also a newish Dickens exhibition there, but I wasn't overly impressed when I saw it. And if you're in Rochester on a Thursday or Friday in summer, the Restoration House and garden.