Pennypack Park in the northeast is nice. It's a narrow stretch of woods that hugs Pennypack creek as it winds for ~8 miles across NE Philly. Paved bike path on one side plus a few trails on both sides. There are entrances at Frankford Ave., Rhawn St., Bustleton Ave., Veree Rd., and Pine Rd. among others. I recommend starting from the nicer Pine Rd. entrance, which I would also guess is closer to you considering you're looking in the Bryn Mawr area. The problem for you would be dealing with traffic to get there. It's also accessible from Rt. 1/Roosevelt Blvd.
If you're willing/able to drive a bit, there's Tyler State Park in Newtown, and Washington's Crossing State Park in PA/NJ. At Wash. X-ing, there are gravel towpaths on both sides of the river, and a bigger park on the NJ side with very nice trails. Worth the drive 2-3 times a month or so.