Following the British recapture of Kanpur during the uprising of 1857, Nana Saheb was widely believed to have sought refuge in which neighbouring region?

The correct option is Nepal.

Historical Context & Role in the 1857 Revolt:
Nana Saheb (born Dhondu Pant) was one of the prominent leaders of the Indian Uprising of 1857. As the adopted son of Peshwa Baji Rao II, he took up arms against the British East India Company in Kanpur after his pension was denied under Lord Dalhousie's Doctrine of Lapse.

Recapture of Kanpur by the British:
In mid-1857, British troops led by General Henry Havelock and later reinforced by Sir Colin Campbell launched a major military campaign to reclaim Kanpur. After fierce battles, the British recaptured the city, forcing Nana Saheb and his key allies to evacuate their stronghold.

Refuge in Nepal:
As the British systematically crushed the rebellion across Northern India during late 1858, Nana Saheb retreated northward into the forested Terai region of neighbouring Nepal.
The British forces were unable to track him down, and he was never captured. It is widely accepted by historians that Nana Saheb spent his final years hiding in Nepal.