Never go to a university just to be close to someone you're involved with, it's not wise.
It's wise to break up. But it's a tricky situation. If you find yourself living in different cities, then you won't be able to have a relationship. The best you can do is remain pen pals and exchange emails and texts, perhaps call each other or video chat or you can even visit each other every once in a while. What I'm saying is that, even though you won't be in a relationship if you're in different cities, it doesn't mean you have to stop contacting each other. Labelling it as a 'break up' seems rather dramatic.
Once again, whatever you do, do not pick a university which isn't your first choice just to be close to him. Your future comes first, the best thing for you would be to apply to your first choice university because that's where you want to be.
If you do choose to move away, then the relationship obviously can't carry on (unless you can somehow find a way to spend lots of time together and to visit each other very regularly, but then this is likely to have a very significant negative impact on your studies). I'll repeat what I said earlier, you can still maintain contact as pen pals by texting and calling each other. But you have to keep in mind that the parameters of your 'relationship' will change drastically.