Hey!
Wow you have a lot of questions.
Its a bit hard to just suggest an accommodation for you, even with all of your requests. The truth is you may apply to one college, not be accepted, and moved to another. This happened to me. I applied to Grizedale super ensuite and got moved to Cartmel.
The gym is miles away, ill just start with that. Never been there but I know where it is :P. Any accommodation you pick, the gym will be far away.
The internet is pretty good, wired its about 750mb/s and wireless its 30mb/s. I do not think it varies at all but I cannot be 100% sure. I play a lot of video games and its fine for me.
The closest to campus would be most of the colleges, expect Cartmel, Londsdale, Pendle posh, and County.
The best accommodation on campus, which is social, is superior ensuite. The beds are fairly long, although they are a single. I am 6"3 and I can only just fit in them.