The town has a population of about 50,000, but it's very compact. The best way to get around is on foot. Everything's within walking distance.
The downtown part of Celje is very old, and very beautiful. There are two churches, as well as an "Old Celje" section. Nearby, but a vehicle is recommended to get to, is the Stari Grad castle. It sits on top of a hill, and the castle was built in the 1400's. One building that's a part of the castle is a tower. The only way to get to the top of the tower is by climbing several steps located inside it, but the climb is worth it. Once on top, the view of Celje is absolutely spectacular and breathtaking.
The obvious thing to do in Celje is simply walk, and take in the amazing views of all the historic buildings they have. If you're missing being near a computer and e-mail, in downtown, they have a cyber cafe. The cost was 150 tolars per hour (around 90 cents). Spend a whole day just walking around, maybe taking pictures. In some places, they have the original cobblestone roads, which are beautiful.