Hi Armie, I attend Spinning classes myself.
If you want a cosy, classy gym, go to Alexander Gym. Not sure of where the branches are, but I do know there's one in Xintiandi.
If you want a budget gym, there's a "neighbourhood" gym in Xuhui Area, which is the one I go to. There're no direct subway stations around, but the nearest station is Damuqiao, and you still have to walk for about 20-30 mins. Or take a bus from Xujiahui Subway. There's Spinning every day at either 7:30 or 7:15pm, depending on which day. The bikes used ARE of the Schwinn brand (which I happen to love too) but they're not in fantastic condition (slightly rusty) but still usable.
PM me if you have more questions
~Sunshine