In addition to tides, currents and submerged structures previously mentioned, commercial traffic on the Delaware River is unforgiving, to maintain course in the channel the tugs and barges will not stop, slowdown or change direction. Anchoring in the river is really not an option.
Neshaminney State Park Marine in Croyden PA, or Winters Sailing Center in Riverside NJ are probably the best options.
In Philadelphia you could try Piers Marina or Philadelphia Marine Center, good access to public transit.
Near the Airport at Essington PA there is an anchorage area protected by Little Tinicum Island and a number of marinas, try Anchorage Marina, also good access to bus service to the airport, and South Philadelphia.