There is some excellent running in the area of Gamlehaugen, a historic royal castle about 6 km south of the center of Bergen. The castle itself has lovely, park-like grounds, where one can put together ~1 km around the paths. Nearby, there are paths that head for ~2 km south — look for the paths that say Paradisstranden, right across the main road from the castle. They lead to Hop Stasjon, a historic railway station. There are also paths that head for ~2 km north, on the eastern side of the Kristianborgvannet lake.
Another good spot in this area is to combine Gamlehaugen with a run around Tveitevannet Lake, about 1.5 km to the east. The perimeter loop is ~2 km, path on the eastern side, roadside path on the western side. Unfortunately, not all of these paths are perfectly connected, but an 8-10 km, very pretty mainly off-road run is possible in this area.