I think people need to start checking the forms first. You can't pick what halls you want. You only pick your preferences (proximity to campus, cost, shared/single, en-suite, self-catered and whatever else there is)
So based on yours, perhaps put self-catered as you main preference, since you don't seem fussed about anything else. Even the furthest UCL halls can be reached within about 20 minutes.
UCL's gym is in UCLU on Gordon Street, and ULU's is at Malet Street, so it'll be just as close as the campus is from your halls. Other gyms, who knows, but they're everywhere.