There are many places to enjoy your drink at Bangkok. Popular bars include Dubliner Irish Pub on Sukhumvit Road or Washington Square. Irish pubs are popular across the world and this is true for Dubliner Irish Pub in Bangkok as well.
The Bull's Head at 33/1, Sukhumvit Road is another popular jaunt. Most ex-pat residents of Bangkok frequent this place. This British-style pub organizes regular theme nights and quizzes too.
The Barbican is another popular bar offering a wide selection of drinks and good food too. This bar is on Soi Thaniya at Silom Road. You can also enjoy a good drink at Vertigo bar of the Banyan Tree Hotel. This hotel is at 21/100 South Sathon Road and the bar is on the 62nd floor.
Some of these pubs disallow smoking during specific hours. Therefore, check beforehand.