Locals tend to frequent shebeens (cheap roadside bars that you'll find across the country) and joining them can be a fast way to make friends. Otherwise, there are a handful of decent bars in the major cities and just about all of the lodges are wonderful places to drink, either from their well-stocked bars or enjoying a sundowner at a carefully chosen vantage point while out on the trail.
What to Drink
Decent locally made beers include Castle Lager (made under licence from the South African brewery), St Louis Special Light and Lion Lager. Also available are the excellent Windhoek Lager (from Namibia) and Zambezi Lager (from Zimbabwe).
Traditional drinks are plentiful. Legal home brews include the common bojalwa, an inexpensive sprouted-sorghum beer that is brewed commercially as Chibuku. Another serious drink is made from fermented marula fruit. Light and nonintoxicating mageu is made from mealies or sorghum mash. Another is madila, a thickened sour milk that is used as a relish or drunk (‘eaten’ would be a more appropriate term) plain.
Mosukujane tea and lengane tea are used to treat headaches/nausea and arthritis respectively. They’re a bit strong in flavour, but locals faithfully tout their remedial properties.
Where to Drink
Maun and Gaborone each have a couple of bars popular with a mixed expat/local crowd, but you're likely to have more memorable drinks at the open-air bars of your accommodation, from the overland feel of the Gweta places to stay, to the quiet and exclusive sunset-facing bars of the lodges and tented camps in the Okavango Delta, Makgadikgadi, Chobe National Park or Central Kalahari Game Reserve.