Last weekend I went to Mt. Avala with the in laws and family. Avala is 18 km south of the city center, and is best reached by car. During the week they are only open till about 430, so you may consider going on the weekend if you are pressed for time. Avala isn’t really a mountain; it’s basically a hill with a recreational park area at top, and a local television tower. There is an elevator that takes you to the top of the tower so you can have a nice 360 view of the surrounding areas. From the top, the view is really fantastic. Beneath you lies a rich, green forest, and surounding that are smaller villages. You can also see Belgrade city center from the top, spot Kalamegdan, the Sava and Danube confluence, and Novi Beograd. Also, on Mt. Avala, there is a hotel, a restaurant, a few snack vendors and picnic benches and such.
A few hundred meters from the tower is the tomb of the Unknown Soldier monument. This is a pyramid style structure made of polished slate stone. Bits of the structure are crumbling off and or missing, and we guessed this might be damage from when the TV tower was bombed during the NATO bombing campaign. Because of these scars, this only moderately impressive structure probably hits home way more with the locals here, than our impressive tomb of the Unknown Soldier does in DC to the locals there.
Avala is something you could consider visiting if you have more than a few weeks in Belgrade. It’s a way to get out of the city and see what local families might do on a weekend.