If you're looking for a more mixed and cosmopolitan crowd, try the downtown/city centre - any of the pubs pouring Slovak beers such as Zlaty Bazant are worth checking out. Alternatively you could go for a great Czech beer on tap - lagers such as Budvar or Pilsner Urquell, Kozel, Radegast, and Starobrno are a few favorites.
There are a number of newer stylish pubs in the centre - not the genuine things but with good beer, decent food and great ambience: Beer Palace in Gorkeho, Sladovna in Venturska. The Dubliner's Irish Pub on Sedlárska Street is popular with tourists and the ex-pat crowd and serves Irish, as well as Slovak beers, along with typical pub style food.
For an unusual presentation of Slovak traditions, visit 1st Slovak Pub on Obchodna street. This pub can accomodate 650 people and is composed of 14 separate rooms representing various periods in Slovakia's history.
Another good place on Obchodna is KGB (stands for Krcma Gurmanov Bratislavy which means Bratislava Bon Vivant Pub). It offers several kinds of beer and lot of great food. Lately, Bratislavsky Mestiansky Pivovar, a microbrewery, opened on Drevena street. It continues the tradition of a well-known brewery from 1752. They brew their own unique beer, Bratislavsky leziak. They also offer wide range of central European dishes.