Petrin Hill is visible from just about anywhere in Prague. It is the large area of grass and trees that rises up on a hill to the west of the River Vltava, just south of the Castle.
There are two options for getting to the top: hiking up one of the many trails, or taking the funicular railway up. Both options involve some steep climbing. Hiking up, one can meander amidst the trees and be treated to an increasingly breathtaking view of the city of Prague to the east. It's about a 20 or 30 minute walk up to the top, and is only mildly strenuous for someone in good health. The funicular railway goes directly up to the top, working on an ancient pulley-like system in which the car coming down the hill pulls the car coming up, and the two balance each other out. At least, this is what I was told. If you're afraid of not being in control on a steep incline, don't opt for this route up. But it's worthwhile to do it once at least. The trip up takes about 4 minutes and the ticket costs 12 Crowns, or about fifty cents US.
Once at the top, there are a couple of attractions that are worth visiting. The main attraction is the Petrin Hill tower, built in the late 1800s and modelled after the Eiffel Tower. This tower is smaller than the Paris version, but still allows for one of the most complete panoramic views of Prague and its surroundings. Admission is about US$4 and the winding stairs going up take about ten minutes to climb. There is a lift available, but I believe this is only for those unable to make the walk up. There are two levels from which to stand and look outward, the most interesting being at the top. It's a nice place to go up and spend a half hour gazing at the architecture and the setting of the city. Try to go on a weekday so that you don't have to fight for space at one of the windows that opens and allows a nice breeze to come through.
At the bottom of the tower, you can sit at a picnic table or on the grass and get the usual assortment of beer, soft drinks, sausages, etc.
Nearby, there's a mirror maze, which, although only asking about US$1 for admission, is not really what it's cracked up to be. Initially, it's quite fun, until one realizes that it's the shortest mirror maze ever created.
To take an alternate route back to where there are buildings, walk west along the "Hunger Wall" named that because it was commisioned to be built largely to give starving citizens paid work. Walking downhill through the trees, you'll eventually come to the Monastery area near the Castle, and from there you can make your way down towards the river through the steep and narrow streets leading down the hill.
Petrin Hill is a great place to spend a few hours and be away from the city. And, for those who are Milan Kundera fans, to get a sense of the location of Tereza's planned execution against a tree.