GPS basic facts
GPS constellation altitude is 20,200km. This is below geosyncronous orbit level; in fact, GPS sats make exactly 2 orbits a day. Furthermore, they are in highly inclined orbits, as opposed to communications satellites, which are in equatorial orbits.
GPS sats beam their signals in fairly tight beams down to the earth's surface (for efficiency purposes), but there is enough spillover that it can be used without problems in low earth orbit. The major modification that is needed to a standard GPS unit to work on the ISS is to remove the "sanity checking" code in the GPS ("gee, I'm several hundred kilometers high, and moving along at over 10,000km/hr. I must be broken!").
Ham radio enthusiasts put a GPS in one of their recent "Oscar" amateur satellites. They found it was even possible to get GPS to work above the level of the constellation, there is enough leakage of signal outwards (and you can detect GPS signals from sats near the edge of the earth) to get good readings.
With a decent antenna, you could get GPS to work on the moon -- well, the parts facing the earth, anyway.