If you're into gardens at all, Sissinghurst is an absolute must! It's mentioned all the time in gardening books and was designed by Vita Sackville-West, a member of the Bloomsbury group. I also really liked Igtham Mote.
If you are ever looking for a fun way to volunteer, NT offers working holidays. They're pretty inexpensive and a lot of fun. I did one on my first visit, and that's what made me want to move over!