The Collaborative International Dictionary of English v.0.48:

classy \classy\ adj.
   1. having elegance or taste or refinement in manners or
      dress. Opposite of styleless. [informal]

   Syn: posh, swish, stylish.
        [WordNet 1.5]

   2. exhibiting refinement and high character. Opposite of
      low-class [informal]

   Syn: high-class. [PJC]

WordNet (r) 3.0 (2006):

classy
    adj 1: elegant and fashionable; "classy clothes"; "a classy
           dame"; "a posh restaurant"; "a swish pastry shop on the
           Rue du Bac"- Julia Child [syn: classy, posh, swish]

Moby Thesaurus II by Grady Ward, 1.0:

55 Moby Thesaurus words for "classy":
   ambitious, braw, chic, clothes-conscious, cosmopolitan, dapper,
   dashing, dressed to advantage, dressed to kill, elegant, exquisite,
   fancy, fashionable, flossy, genteel, high-flown, high-flying,
   high-toned, highfalutin, highfaluting, in, jaunty, lofty, modish,
   natty, neat, nifty, nobby, ostentatious, posh, pretentious,
   recherche, ritzy, sharp, sleek, smart, smug, snazzy, soigne,
   soignee, sophisticated, spiffy, spruce, style-conscious, swank,
   swanky, swell, swish, tony, tricksy, trig, trim, vaunting,
   well-dressed, well-groomed