Have you looked at East Falls or Manayunk? Both of these neighborhoods offer pretty easy access to the river trail, and the stretches of the trail passing through them are very popular with runners and cyclists without being too crowded (compared to the parts closer to Center City). Both would we within your price range, and they're pretty safe neighborhoods. East Falls has a little more of a suburban feel, and has fewer shops/restaurants, while Manayunk has a pretty thriving main street. Manayunk also has a reputation for having a lot of recently graduated college students living/partying there, but that probably varies block by block.

Don't know if you have a car, but parking in both neighborhoods can be a challenge, especially Manayunk. Based on your comments on safety, you may also want to consider that little pocket of a neighborhood where the old Pep Boys headquarters is (it's just southeast of East Falls, along Allegheny Ave). There's some new construction going up, so if you're looking for value you could probably get it there. That said, the neighborhood is in the very early stages of developing, so you'd be looking at 5 or so years minimum before meaningful improvement. Still provides easy access to the river trail, though.