Varanasi is a temple city and officially alcohol-free in the ghats area — do not expect a bar culture. What the city does well is chai and rooftop cafes with river views.
Prinsep Bar (Brijrama Palace Hotel) — One of the few respectable places to get a drink in the city, inside a heritage hotel overlooking the Ganges. Expensive by local standards but atmospheric.
Rooftop Cafes at Assi Ghat — Several rooftop restaurants overlook the ghat here, ranging from basic to comfortable. Brown Bread Bakery is a favourite with long-term travellers: good coffee, decent Western food, and a yoga studio upstairs.
Chai at any ghat — The authentic Varanasi experience is sitting cross-legged at the top of a ghat with a tiny clay cup of chai watching the Ganges at dawn. The earthenware cups (kulhar) are meant to be smashed after use — a biodegradable Subcontinental tradition.