Mae govannen, mellyn nin!

This is my first post here, but long have I watched the goings on from the comfort of my hobbit hole. I will shortly be leaving the US for the first time to partake in a summer course at Oxford, taught by John Garth himself! I must confess I'm probably on the youngest end of the spectrum here, so my familiarity with Tolkien beyond his fiction is rather limited (but I have my whole life ahead of me to amend that), and thus I seek the sage advice of you loremasters as to what Tolkien sites I should include in my visit to England. I greatly appreciate any recommendations you can offer!