WordNet (r) 3.0 (2006):

stay put
    v 1: stay put (in a certain place); "We are staying in Detroit;
         we are not moving to Cincinnati"; "Stay put in the corner
         here!"; "Stick around and you will learn something!" [syn:
         stay, stick, stick around, stay put] [ant: move]

Moby Thesaurus II by Grady Ward, 1.0:

64 Moby Thesaurus words for "stay put":
   abide, adhere, agglomerate, be still, be unflappable, bunch, clasp,
   cleave, clinch, cling, cling to, clot, cluster, coagulate, coast,
   cohere, congeal, conglomerate, embrace, freeze, freeze to,
   get home free, grasp, grow together, hang on, hang together, hold,
   hold fast, hold on, hold out, hold together, hold up, hug,
   keep quiet, lie still, mark time, mass, not breathe, not budge,
   not stir, persist, remain, remain firm, remain motionless, repose,
   rest, ride it out, set, solidify, stand, stand fast, stand firm,
   stand pat, stand still, stay, stick, stick fast, stick it out,
   stick together, take hold of, tarry, tread water, weather,
   weather the storm