Varsity is supposedly a "pub" but whenever I've been it's more sort of modern music and cheap drinks. Not very pub-like really. There is a pub being built on campus with the union rebuild, but since it's part of the union it'll be a student pub, which kind of changes the atmosphere.
In your second year you'll most likely want to be in Leamington (at least most people do) so you could check that out to see if it'd be worth putting up with a year of the campus. If you really want to leave campus you can but it's just a pain with buses and stuff. Birmingham is quite close too, and only cost me £3 to get there the other night.