My university has a gym, but it's tiny. Where I am though, I can buy a gym membership that covers the uni gym, the local gym, swimming pools and athletics track. I paid £75 I think for one year so a great deal really. I use the local gym because it's bigger, has more machines/space and a separate weights room.
As for quiet times, I always find that 10am-12pm, 2pm-4pm, 7pm onwards are quiet. Best times are definitely Friday/Saturday evenings or Monday mornings!