You did not say that you did not have an Internet connection and a computer with a browser. If you knew the name of the underground facility and they where in USA, the guards and the staff probably have a licensed surface transmitter licensed by the American FCC. The transmitter is for surface perimeter security and staff trips to the local store for supplies. You can go to the FCC database and look up the license by name and it will give you the lat/long coordinates and physical address. However, if you have the physical address of the facility there are Internet programs that convert physical address to lat/long coordinates.
You also did not say whether you were allowed to stick your head up out of the surface doorway to look at the sun. Knowing the correct time and the local sun angle you could compute rough position. You could use your hand as a rudimentary protractor. If you knew what hemisphere you where in then you could compute the sun's angle toward the equator. (Note: if there is an overcast day and you can not see the sun use a polarized light filter to locate the sun behind the clouds - similar to the Viking SunStone or cordierite crystal)
If you had an airplane altimeter you might be able to determine your sea level. You can make a homemade altimeter at: http://www.ehow.com/way_6467568_homemade-altimeter.html
However, if there is a elevator (or vertical ventilation shaft), go the the shaft and whistle loudly. The time it takes for the return echo is the distance to the top. Sound travels at 1,100 feet per second. So divide the time it takes from you whistling until you hear the return by half. And then do the math to compute your depth below ground. The echo is bouncing off of the elevator's floor or the ventilation shaft's hood. Send the elevator to top floor first.
Or you could drop a medium-sized rock or metal ball bearing into the shaft from the top floor. Listen for the sound of the crash. Objects (unaffected by air disturbance like a feather) fall at 300 feet per second. The return sound traveled at 1,110 feet per second. If you have a stopwatch you could compute the distance to the bottom. I don't feel like doing the algorithm for that. You can do it I'm sure.