The Neckar Valley east of Heidelberg is one of the most scenic stretches of river in southern Germany. The valley road and the railway line pass through a succession of wine villages — Neckargemünd, Mosbach, Hirschhorn — each with a hilltop castle above the vine-terraced slopes. Eberbach, about 40km east, has a fine old town and a Cistercian monastery worth a stop. The valley is best explored by bicycle (the Neckartal-Radweg runs the full length) or by one of the historic steam trains that operate on summer weekends.
Mannheim, 20km north, is reachable in 15 minutes by S-Bahn and makes an interesting contrast: a Baroque planned city laid out on a strict grid, with the largest palace in Germany after Versailles. The Kunsthalle Mannheim has a strong collection of 19th and early 20th century German painting. The city is also the starting point for Rhine cruises.
Stuttgart, the state capital of Baden-Württemberg, is 80km south and about 40 minutes by ICE train. The Staatsgalerie is one of Germany's best art museums, the Porsche and Mercedes-Benz museums are just outside the centre, and the city's Württemberg wine country fills the surrounding hills. A day trip is easily done and well worth it, particularly if the Heidelberg crowds are getting heavy.
Speyer, 30km southwest across the Rhine, has one of the finest Romanesque cathedrals in Europe — the Kaiserdom, a UNESCO World Heritage Site — and the excellent Technik Museum with a real space shuttle on display. Worms, another 20km north along the Rhine, has the cathedral where Luther refused to recant in 1521.