Berhampur's appeal is largely in what is around it.
Gopalpur-on-Sea (16 km south-east) — once an ancient seaport and an Anglo-Indian seaside resort under the British, now a sleepy beach town with a long, broad strand and a small fishing harbour. Far quieter than Puri to the north, and far better for a real swim and walk. Stay overnight if you can; the seafront at dusk is the best argument for being in coastal Odisha.
Taptapani (50 km west) — a hot sulphur spring set in low forested hills, where a stone bathing pool collects the water at a temperature just bearable for soaking. Popular with pilgrims and Indian holidaymakers; basic accommodation is available if you want to come for a night.
Jaugarh (35 km north) — the site of one of the Ashokan rock edicts, a third-century BC pronouncement of the Mauryan emperor Ashoka carved into a boulder at the foot of a low hill. Of great historical importance and almost completely untouristed.
Chilika Lake — Asia's largest brackish lagoon, accessible from the northern Odisha coast around Rambha (about 60 km north of Berhampur). Famous for migratory birds in winter, Irrawaddy dolphins, and quiet boat trips out to small islands.