Alcohol is available in Leh — this is not a dry destination — but the scene is low-key. Most travellers drink at their guesthouses or at the handful of restaurants that serve beer. Chang, the local barley beer, is worth trying if you encounter it at a local household; it is rarely on restaurant menus.
Cafe Jeevan near the main bazaar is a good daytime stop for espresso and decent filter coffee, which is genuinely hard to find in the mountains. It also does good breakfast and light lunches.
The Bookworm Cafe in Changspa has a library of well-worn paperbacks, strong tea, and a sociable terrace where trekkers compare routes and compare altitude horror stories. Beer is available.
Lehchen Bar is one of the few places specifically set up as a bar rather than a restaurant that also serves drinks. Local and Indian beer, some spirits, and a terrace that makes the most of the clear mountain evenings.
Most serious drinking happens at guesthouse rooftops after dark. Kingfisher and Tuborg are ubiquitous; ask for Seabuckthorn juice if you want something local and non-alcoholic — it is made from the bright orange berries that grow wild along the Indus riverbanks.