You have allll of Europe at your fingertips! Things to think about are what sort of budget you have, how long you'd like to stay, and how comfortable you feel when you don't speak the local language.
If you don't mind being "snug" there are lots of no-frills airlines that operate out of numerous airports in England (Ryan Air, EasyJet, Jet2, bmibaby, possibly someone else can name some more). Being on a student budget, I've always just gone with whatever city ends up being cheapest. It hasn't done me wrong (yet).
Personally, I prefer big cities, since they're vibrant, fun, and there's always something to do! As far as specific places; I must say my favorite places so far were Madrid and Athens--but we went in the spring when it was a bit warmer. Rome was too tourist-y for me, but one of the things I love most about travelling is trying the local cuisine. So definitely wherever you end up going, try to immerse yourself into your chosen destination's culture, by watching what the locals do/ordering what the locals order. Either way, I'm sure a group of 23-25 year olds will have an absolute blast!