When should I tune my piano after a move?

Moving a piano in itself shouldn't make it go out of tune, provided it gets tuned regularly by a competent tuner.  In other words the vibration to the the piano caused by moving shouldn't affect a well tuned (ie. stable) instrument.  However there may be an environmental effect of differences in temperature and humidity during the move and at the receiving end that are significant enough to affect the pitch or the unisons or both.  If a piano is moved within it's local environment to a room with similar temperature and humidity in a brief period of time (1-2 hours) and isn't overly stressed during the process it shouldn't need extra tunings other than its regular 6 - 12 month period.  Of course you need to use your ears to determine if it sounds out of tune, and for many pianos that don't get tuned regularly moving is a great excuse for getting back on track.  I usually recommend a couple week acclimation period before tuning after a move - not because it actually takes that long to reacclimate to a new environment (it really only takes a few hours) - it just seems like a good amount of time for everybody to settle in and get used to a new environment, and occasionally there are extenuating factors which aren't accounted for like a piano being stored in a garage with extreme humidty (or lack) - or moving from a coastal environment or other extreme which can take more time.