Quite close to Pristina is the Gazimestan Tower. It is a monument that commemorates the 1389 Battle of Kosovo, the battle in which Sultan Murad I was killed.
Bring an ID, which will be logged by a guard on entry. Look for the Kosovo curse written in cyrillic on the base. You can climb several flights of stairs to get to the top. The vantage point is nice, but there is not much to view. There is a metal plaque at the top showing the details of the Battle of Kosovo. It is a quick, nice trip.
Tip: Sultan Murad I’s Tomb is just nearby. You can do both sights in one day.
Learn about it before you go: http://en.wikipedia.org/wiki/Gazimestan
Driving Directions: (~10-15 mins) Starting at U.S. Embassy Bravo gate, drive right down hill to the main road (Ahmet Krasniqi). Continue to the first traffic circle. Go straight through past Te Ismeti hardware store, choosing the first option toward Mitrovica. In just a few kilometers, you will see a brown sign with white lettering that says, “Gazimestan.” Take the right and park outside the gate to the tower.