Yes Going west means going to Dushu Lake Campus of Suda University, passing through or bypassing Dushu Lake School of Suda University, and you will see Dushu Lake Gymnasium, which has a gym.

It's a little far. I suggest you go by bike. It will take you 5 minutes. If you don't know the direction, you can ask people on the roadside how to get to Dushu Lake Gymnasium. The location is obvious and easy to find.