My husband will be in London on business and I am thinking of taking vacation time to go with him. We will be based in London but I don't know which hotel. I have been to London several times already and am looking to sightsee outside of the city. I have been to Windsor and Hampton Court. I read that British Rail has day passes (2 day, 4 day) for the London vicinity so this sounds attractive. £28 for all 4 days I think. I've always wanted to see Canterbury Cathedral but I'm also interested in Arundel and Leeds Castles (respectively) and seeing coastal Dover as I have always wanted to see those white cliffs.

I will be travelling alone but I'm quite train savvy. I don't want to rent a car so I hope I can see these landmarks via train.
Thoughts? What can I do in a day? What can I combine in a day? Thank you.