Call before you dig #811. Usually a free service. Cheaper for utliliies to mark locations of pipe for free than repair broken pipes.
is that a joke?!?!
Anyway,
Not drill all the way through???

How do you know how deep the tubing is?
Is the heating system operational? If so, can you get your hands on a thermal imager - infrared thermo gun might work too.
These tools would pick up on the hottest part of the concrete (where the tubing is)
The IR gun would probably be the easiest to find, hell you can buy 'em now for less than $100.
The thermal imager would be more accurate, shows you an actual picture of the heat. Many fire depts use them for locating people in fires (heavy smoke = zero visibility), perhaps they would stop by with it for small donation. I have one at work (used to locate hot spots on high voltage equip) that is sensitive enough to show the footprints of where a person was standing minutes after they've left.