The Buda Protected Landscape Area covers a large sweep of wooded hills, valleys, and limestone slopes on the western side of Budapest. It includes some of the city's easiest escapes into nature, with walking routes that can be as short or as long as you want.
Use it as a frame for hikes around the Buda Hills rather than as one single destination. The Children's Railway, Zugliget chairlift, and several hilltop viewpoints make good access points.