The Baths at Bath are absolutely awesome... the audio tour is so worth it. It is about 9 pounds for students, don't know what the regular price is. I also love Liverpool... it is sooo fun at night. I can't remember where I went when I was there, probably because I was drunk. Still... fantastic city. Stratford is also pretty neat, but very touristy. You don't need long to see it.
I like Cambridge better than Oxford... you can't like both
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Have a great time... I am soooo jealous.