Ashgabat is not a city with a bar culture. Alcohol is technically legal but the state has periodically restricted its sale and display, and the social infrastructure for casual drinking — the pub, the wine bar, the street-side cafe with beer — does not exist here in any recognisable form. What exists instead is a set of hotel bars operating for foreign guests and business travellers, and a handful of licensed restaurants where beer and vodka are available alongside food.
The cafe culture is similarly constrained. There are modern coffee shops in the marble city catering to the small expatriate and government-adjacent professional class, but they are not easy to find independently and their operating hours are unpredictable. Tea — green tea (gok chay), served in small bowls without milk — is the universal social drink, available everywhere and excellent. If your guide takes you to a chaykhana (teahouse), the tea will be better than anything from an espresso machine.