Heidelberg is a fun town to explore on a daytrip. The historic old town has lots of restaurants, cafés and little stores. The highlight of the city is the castle on the hill above the city with a beautiful view over the city and the river. It's an hour from Kaiserslautern by car but can easily be reached by public transportation as well.
Burg Eltz (Eltz castle) is a very popular medieval castle in the area. It's close to the wine region along the Moselle and Rhine and it can be easily combined with a trip to Bacharach, Bernkastel-Kues, etc. There are also several hiking trails surrounding the castle. The castle is a 2 hour drive from Kaiserslautern.
Strasbourg is a beautiful French city by the Rhine river close to the German border. It has lots of restaurants, bakeries, stores and the famous cathedral. It's a two hour drive from Kaiserslautern.
The Moselle and Rhine valley are famous for wine and castles. Along the river(s) you will find lots of cute little towns with half-timbered style houses (Fachwerkhaus) and great wine. Some of my favorite cities are Bacharach (the picture at the top), Bernkastel-Kues and Cochem. Cochem has a beautiful castle that is open to visit and lots of river cruises departing from the city. All cities mentioned above are within a two hour drive range from Kaiserslautern and can be easily combined with a visit of Eltz Castle.
Trier is a historic city close to the Luxembourg border. Founded by the Romans, it contains several well-preserved Roman structures like the Porta Nigra gate, the ruins of Roman baths, an amphitheater just outside the center and a stone bridge over the Moselle River. Trier is a 1 hour 20 minute car ride from Kaiserslautern or two hours by train.
Annweiler is situated in the Southern part of the Palatinate forest called the Wasgau, and is surrounded by high hills which yield a famous red sandstone. There are many hiking trails in the region and the city has a beautiful old town. One of the highlights is the Trifels castle, a reconstructed medieval castle on a hill above the city. Annweiler am Trifels is about 45 minutes by car from Kaiserslautern.
Neustadt is surrounded by pretty vineyards at the heart of the German Wine Route and a firm favourite among tourists for its romantic, half-timbered old town and historic hilltop castle. The city can be easily reached by public transportation in 30 minutes or by a 45 minute drive.
For racing fans: the famous Nürburgring is two hours north of Kaiserslautern. Additionally to the race tracks there is a museum, a small castle and go kart options.