Is it open early mornings/late at night? And, though you might not want to walk, is it close enough to take a morning/late night jog to?
Edit: Spouse wants to know if law student spouse's are able to go too.
The AFC opens 6am until midnight during the week. Slightly fewer hours at the weekend.
The area around the AFC is usually busy, lots of undergraduate housing there. There's quieter parts on the route between the law school and the AFC. You might not want to jog between the law school and AFC alone in the dark.
Unless you're looking to swim, many of the facilities are available in the North Grounds gym which is very close to the law school. It has similar, though not identical hours.
Spouses of students can join - $90 / 4 months.