Singani is Bolivia's national spirit — a grape distillate produced at altitude in the Tarija region, legally protected under Bolivian law much as pisco is in Peru. It tastes lighter and more floral than pisco, and at altitude it hits faster than you expect. The classic preparation is a chuflay: singani with ginger ale and lime, served long. Sopocachi is where the better bars tend to be, several of which have made singani cocktails their focus.
The bar scene around Plaza Avaroa and the streets behind it is where to start. Altitude affects alcohol significantly — a rough rule is that two drinks at 3,600 metres equal three at sea level, and the effects build over an hour or two. Drink slowly and eat well. On weekends the bars stay open late; on weeknights the pace is more sedate. Prices are very reasonable by international standards.