The Collaborative International Dictionary of English v.0.48:

Stadium \Sta"di*um\ (st[=a]"d[i^]*[u^]m), n.; pl. Stadia
   (st[=a]"d[i^]*[.a]). [L., a stadium (in sense 1), from Gr.
   sta`dion.]
   1. A Greek measure of length, being the chief one used for
      itinerary distances, also adopted by the Romans for
      nautical and astronomical measurements. It was equal to
      600 Greek or 625 Roman feet, or 125 Roman paces, or to 606
      feet 9 inches English. This was also called the Olympic
      stadium, as being the exact length of the foot-race
      course at Olympia. --Dr. W. Smith.
      [1913 Webster]

   2. Hence: A race course; especially, the Olympic course for
      foot races.
      [1913 Webster]

   3. Hence: A modern structure, with its inclosure, resembling
      the ancient stadium[2], used for athletic games which are
      typically played out-of-doors; such stadiums are usually
      large structures without roofs, though some modern
      stadiums may have a protective dome overhead. It may be
      contrasted with the arena, the term commonly used for
      smaller structures at which indoor games are played.
      [Webster 1913 Suppl. +PJC]

   4. A kind of telemeter for measuring the distance of an
      object of known dimensions, by observing the angle it
      subtends; especially (Surveying), a graduated rod used to
      measure the distance of the place where it stands from an
      instrument having a telescope, by observing the number of
      the graduations of the rod that are seen between certain
      parallel wires (stadia wires) in the field of view of the
      telescope; -- also called stadia, and stadia rod.
      [1913 Webster]

WordNet (r) 3.0 (2006):

stadium
    n 1: a large structure for open-air sports or entertainments
         [syn: stadium, bowl, arena, sports stadium]

Moby Thesaurus II by Grady Ward, 1.0:

71 Moby Thesaurus words for "stadium":
   agora, amphitheater, arena, assembly hall, athletic field,
   auditorium, background, bear garden, bowl, boxing ring, bull ring,
   campus, canvas, chapel, circus, cockpit, coliseum, colosseum,
   concert hall, convention hall, course, dance hall, exhibition hall,
   field, floor, forum, gallery, garden, ground, gym, gymnasium, hall,
   hippodrome, lecture hall, lists, locale, marketplace, mat,
   meetinghouse, milieu, music hall, open forum, opera house,
   palaestra, parade ground, pit, place, platform, precinct,
   prize ring, public square, purlieu, range, ring, scene,
   scene of action, scenery, setting, site, sphere, spy,
   squared circle, stage, stage set, stage setting, terrain, theater,
   tilting ground, tiltyard, walk, wrestling ring