The most popular day trip from Cuddapah is the Gandikota gorge, about 75 kilometres north — a dramatic limestone canyon cut by the Pennar River, sometimes called "the Grand Canyon of India" with the usual overstatement, but genuinely impressive. The ruins of a 13th-century Vijayanagara-era fort sit on the gorge rim and are worth combining with the canyon view. Plan an early start and the whole day.
The Belum Caves — the second-longest cave system in India — are 75 kilometres west and a half-day if you start early. The temple town of Pushpagiri, about 15 kilometres from Cuddapah, has several 13th- and 14th-century temples in good condition and is a short morning out. The road north toward Lepakshi and the Sri Sailam region is longer but possible as a long day from Cuddapah if you want to push it.