In the northern part of the Spandau borough, there’s some nice running in the Spandauer Forst (forest) and the Uferpromenade path along the upper part of the Havel River. They are adjacent and can be run separately or mixed. Also, a ferry crosses 160 meters of the Havel River connecting the Spandau and Reinickendorf districts, where you can access the Tegeler Forst & Tegeler See (lake) area.
 
Spandauer Forst is another of Berlin’s large forest parks. The paths are mainly wooded, with some open fields, and a path along the narrow Kuhlake Stream. One can also follow a path (part of it paved) along the Brandenbrg Wall, which runs mainly around the perimeter of the park, making for a ~9.5 km loop! Good maps and loop options are located right off the parking lot at Schoenwalden Allee.
 
Uferpromenade. Google Street View

Havel River Path. A pleasant path runs along the Havel River in the northern part of Spandau, near the Berlin-Brandenburg border. It goes from the Tegeler See (Hakenfelde) ferry stop north for 9.6 km to Hennigsdorf. Most of the path is paved and runs right alongside the river, with nice water views. There are a couple of short sections away from the water. At the 4.5 km mark is a small bridge that must be crossed to continue. 

  • ACCESS FROM SPANDAUER FORST: Best access is from the southeast end. Cross Niederneuendorfer Allee onto Rustweg.