Fortunately there were footpaths on the hillside leading right to the castle and beyond the main gate we were able to run all over the castle grounds. There were a few pedestrians around. From several vantage points we had great views over Brescia and the castle itself is pretty solid and impressive.
When we came down the castle hill we realised we had come down in the wrong place. But instead of retracing our steps we headed for another of Brescia's landmarks, the Capitolo. We couldn't go inside the grounds of the adjacent Roman temple and amphitheatre ruins but the Capitolo itself, with its partially reconstructed columns and roof, looked very fine.
We finished the run by crossing the Duomo (well, actually old and new duomo's) square.