Chandigarh sits at the foot of the Shivalik Hills and is the obvious gateway to several worthwhile day trips. The big two are Shimla, the old summer capital of British India, three hours' drive into the mountains, and Pinjore Gardens (Yadavindra Gardens) just east of the city, a terraced Mughal garden laid out in the 17th century that makes a pleasant half-day escape.
Further afield, Anandpur Sahib is one of the holiest places in Sikhism and about two hours by road; the Virasat-e-Khalsa museum here, designed by Moshe Safdie, is one of the most striking modern buildings in northern India. Amritsar and the Golden Temple are reachable as a long day trip but really deserve an overnight.