Distance from the centre is no issue at all, aside from when it's raining and you have to get to a library and the last thing you want to do is walk for 20 minutes. If you have a bike, you'll be fine, though, and frankly I think I'd also be loath even to walk for 5 minutes in the rain so I'm not sure it makes all that much difference.
Plenty of people have friends in other colleges, and as things go I haven't found it a hindrance socially. Don't worry about it—and congrats on the offer.