All six verified Varanasi hotels are Team Verified, spread between the ghats and the old city near Kashi Vishwanath Temple, with pet charges ranging from nothing to a five-star fee.
Hotel Buddha Park, Hotel Ganges View at Assi Ghat, Mahant Ji Residency, and The White Canyon Hotel all confirm no additional pet charge. Local Lok Varanasi charges a modest ₹200 a night. Taj Ganges is the outlier, a five-star property with vast green lawns charging ₹3,000 plus GST, one of the few luxury stays in the city that formally accepts dogs at all.
Given how many of these are free, location relative to the ghats you actually want to visit is probably the more useful way to choose.