Mount Davidson has many trails to walk on from foresty and immersive to rocky and calm. Each trail is easy to moderate difficulty for hiking, though weather conditions can increase the diffuculty of these hikes.
You can visit the famous big white cross at the peak of the mountain. There are also various other places atop the mountatin to see such as the views of the iconic Sutro tower and beautiful view of the downtown.
The trails closest to the Muni stops are the Sherwood Trail or the Jaunita Trail. The Sherwood trail is the main one that leads to the views and the cross, but other trails offer a more foresty feel as the trails are surrounded by natural life.
It is worthy note that the Juanita Trail, Cresta Vista Trail, and the Rockdale Trail are more on the foresty side of walking, so there may be rose bush thorns and slopes to watch out for. Note that sometimes reception can be blocked off on these trails but they are not difficult to navigate.