In the unlikely case that you get bored by Heidelberg itself, or, in the more likely case that you find it too difficult to find your way through other tourists who are interested in the famous city, you will find a lot of interesting destinations in relatively short distance from Heidelberg.
If you follow the deep valley of the river of Neckar upstream (by boat, bicycle or car) you find a chain of little Romanesque castles (e.g. in Hirschhorn, Dillsberg, Neckarsteinach (4 castles)).
A 20 km trip brings you to village of Mauer where 1907 human jaw-bones were found which later proved to be the earliest reference of human being in Europe - the 600000 years old Homo heidelbergensis.
Concerning cultural-historical interests, one must further mention the Palace of Mannheim (about 20 km), the Palace and Gardens of Schwetzingen (about 20 km), or the famous 850-year-old Monastery of Maulbronn (60 km), which is often cited as the best-preserved medieval monastery complex north of the Alps.
Heidelberg is also not far from other fascinating places of German history. A visit to the City of Trier will bring you close to the very early German history, when Germany still has been "Germania" and the Romans ruled the area west of the Rhine river. Trier has been claimed to be the "Oldest City in Germany". In the City of Speyer you will find one of the greatest German treasures of Romanesque architecture - the imprial Speyer Cathedral ("Dom zu Speyer") which has been built in the years 1030-1061. The City of Mainz is most known for her son Johannes Gutenberg who is the inventor of movable type printing. Karlsruhe is known for its beautiful palace and gardens.
The closest bigger towns (in German standards) are the cities of Mannheim (350000 inhabitants, 30km) and Frankfurt (600000 inbhaitants, 80km)
Last not least, the location of Heidelberg provides the possibility that, if you like to escape from Germany or its inhabitants for a little while, you will reach the French border within a less-than one-hour car ride.
France or e.g. the famous City of Strasbourg might let you take part in the French way of life and offer you cuisine Francaise with vin rouge and, of course, many more serious treasures of the French culture.