The big day trip is Fatehpur Sikri, 37 km west, easily combined with the Mughal capital ruins of Bharatpur and the Keoladeo National Park (a UNESCO wetland and one of India's best bird-watching sites, especially November to February) just across the Rajasthan border.
Mathura and Vrindavan, 50 km north, are sacred to the god Krishna and full of working temples, ghats, and pilgrims. The atmosphere is intensely Hindu — Vrindavan in particular is sometimes called the city of widows.
Gwalior, 120 km south, is a longer day or overnight trip — a magnificent hilltop fort, Jain rock-cut sculptures along the access road, and the haveli mansions of the Scindia dynasty. The Shatabdi express makes the run in 75 minutes.