Spring — April to early June — is the best time to visit Heidelberg. The hillside forests are coming back into leaf, the days are long enough to linger on the Alte Brücke at sunset, and the tourist crowds have not yet peaked. The university is in session, so the city has its student energy intact. Early June also marks the first of the three annual Schlossbeleuchtung fireworks nights, when the castle is illuminated over the river in a tradition dating back to 1830.
Summer (July and August) is the busiest period. The Hauptstrasse fills with tour groups by mid-morning, parking is difficult, and accommodation prices rise sharply. That said, the weather is reliably warm, the Rhine-Neckar plain is sunny, and open-air events fill the calendar. The second and third Schlossbeleuchtung nights fall in July and September respectively, and are worth planning around.
Autumn is underrated. October brings the wine harvest from the surrounding Neckar Valley villages, the beech forests on the Königstuhl turn copper and gold, and the pace drops to something more comfortable. Winter is quiet — cold and occasionally foggy in the Rhine plain — but December brings a well-regarded Christmas market on the Marktplatz and in the castle courtyard.