Swimming in the Aare in summer is well nice.

Actually near Monbijou, there are a number of fitness centres & at least one pool that I'm aware of.

If you are into cycling, Bern is perfect, as we have paths on both side of the river that go on for miles/klms. Favourite for me is from Bern - Thun, all the way on the river 35k work out with a dip in the Thunersee at the other end.

Let me know if you need any more info, will help where I can.

P