The Collaborative International Dictionary of English v.0.48:

Gymnasium \Gym*na"si*um\ (j[i^]m*n[=a]"z[i^]*[u^]m or
   j[i^]m*n[=a]"zh[i^]*[u^]m; 277) n.; pl. E. Gymnasiums
   (j[i^]m*n[=a]"z[i^]*[u^]mz), L. Gymnasia
   (j[i^]m*n[=a]"z[i^]*[.a]). [L., fr. Gr. gymna`sion, fr.
   gymna`zein to exercise (naked), fr. gymo`s naked.]
   1. A place or building where athletic exercises are
      performed; a school for gymnastics.
      [1913 Webster]

   2. A school for the higher branches of literature and
      science; a preparatory school for the university; -- used
      esp. of German schools of this kind.
      [1913 Webster]

            More like ordinary schools of gymnasia than
            universities.                         --Hallam.
      [1913 Webster]

WordNet (r) 3.0 (2006):

Gymnasium
    n 1: a school for students intermediate between elementary
         school and college; usually grades 9 to 12 [syn: secondary
         school, lyceum, lycee, Gymnasium, middle school]
    2: athletic facility equipped for sports or physical training
       [syn: gymnasium, gym]

Moby Thesaurus II by Grady Ward, 1.0:

105 Moby Thesaurus words for "gymnasium":
   agora, amphitheater, archery ground, arena, athletic field,
   auditorium, background, badminton court, baseball field,
   basketball court, bear garden, billiard parlor, bowl,
   bowling alley, bowling green, boxing ring, bull ring, campus,
   canvas, circus, cockpit, coliseum, colosseum, course, court,
   cricket ground, croquet ground, croquet lawn, diamond, fairway,
   family room, fencing school, field, floor, football field, forum,
   game room, glaciarium, golf course, golf links, gridiron, ground,
   gym, hall, hippodrome, ice rink, infield, links, lists, locale,
   marketplace, mat, milieu, open forum, outfield, oval, palaestra,
   parade ground, pit, place, platform, playground, playing field,
   playroom, polo ground, pool hall, poolroom, precinct, prize ring,
   public square, purlieu, putting green, racecourse, racket court,
   range, rec room, recreation room, ring, rink, rumpus room, scene,
   scene of action, scenery, setting, site, skating rink,
   soccer field, sphere, squared circle, squash court, stadium, stage,
   stage set, stage setting, stretch, tennis court, terrain, theater,
   tilting ground, tiltyard, track, turf, walk, wrestling ring,
   wrestling school