Puno's bar scene is concentrated on Jirón Lima and the streets immediately around it. Most places stay open till around midnight; the city as a whole goes to bed early. Pisco sours are the standard, and several of the bars on Lima do decent ones; coca sours (made with macerated coca leaves) are a local twist worth a try at least once.
Mojsa Restaurant has the best cocktails in the city centre and a warm interior; Kamizaraky Rock Pub draws a younger Peruvian-and-backpacker crowd; Café Bar de la Casa del Corregidor has good coffee, a quiet courtyard, and a strong wine list. For a coffee morning, La Casona on Jirón Lima and Ricos Pan are both reliable.