2002 3100 V6 Losing Coolant

Hello one and all!
My 2002 has had a slow coolant leak for quite a while (maybe a quart a month)
Now, however, I am losing over a gallon a week, but with NO visible leak!
The oil is clear, with no signs of antifreeze in it, so I am guessing the head gaskets are ok. But I am perplexed as to where my coolant is going!

Any ideas???
Thanks!

EDIT: After reading more threads in the forum, (which I should have done more thoroughly before posting,) it seems that I may indeed have a head gasket leak. From what I've learned, that would cause me to lose coolant through the exhaust while driving, and would explain why I don't see a visible leak anywhere. Am I on the right track? Before I replace the head gaskets, are there any other causes that may have a simpler fix??

I would rent/buy or borrow a cooling system pressure tester. Look closely around the intake gaskets, especially under the throttle body area where the intake meets the block. Also, check under the right side of the dash for damp carpet or any other traces of coolant that may indicate a heater core leak. There are also testers that will check for Hydrocarbons (exhaust gases) in the coolant to help verify a head gasket leak.

The carpet under the heater core is bone dry. While there is a slight oil residue buildup under the throttle body, it is dry as well. Looking there, it appears the oil residue is coming from the valve cover gasket near the ECT.
What would cooling system pressures expect to be? As far as I know, the pressure should be below 15psi in my car, but how would I know what is an acceptable pressure?

Another "symptom" ?? I fillled and bled the cooling system this morning, and now, after over an hour of idling with occasional throttle around 2,000 rpm, my tailpipe is wet. Puddled and dripping. But, it's water only, not antifreeze.
But it is a lot in the pipe. Finger is literally wet as if I put it in a glass of water.

The carpet under the heater core is bone dry. While there is a slight oil residue buildup under the throttle body, it is dry as well. Looking there, it appears the oil residue is coming from the valve cover gasket near the ECT.
What would cooling system pressures expect to be? As far as I know, the pressure should be below 15psi in my car, but how would I know what is an acceptable pressure?

Another "symptom" ?? I fillled and bled the cooling system this morning, and now, after over an hour of idling with occasional throttle around 2,000 rpm, my tailpipe is wet. Puddled and dripping. But, it's water only, not antifreeze.
But it is a lot in the pipe. Finger is literally wet as if I put it in a glass of water.

The pressure tester allows you to pressurize the system without the engine running, and leave it pressurized to check for leaks. Yes, your cap probably releases pressure at 15psi. As far as the water in the tail pipe, I would chalk it up to normal condensation from the exhaust...

I will investigate renting one. Thank you. Although I have a feeling I'm in for a big repair, I'm hoping it's something minor. I'd rather exhaust the less expensive options before I commit to replacing the head gaskets only to find that the problem still exists.
Thanks for the answers, gmtech.
Time to do more testing.

To lose a gallon a week is significant....

So, as GMTech1 suggested, get a coolant pressure tester, and see if the pressure drops.....if it doesn't, leave it pressurized overnight, if needed.....

Check the radiator, w/p weep hole, radiator and heater core hoses/clamps, condensate drain, and especially the lower intake gaskets....look especially under the throttle body....there are depressions in the top of the engine where it can collect....also under the PS pump, where it can trickle down the front and rear of the engine....

If a head gasket goes, more often than not it is #1 cylinder(passenger side, rear of the engine).....check for a leak in the gasket in that area....

If you see no external leaks, then it's possible you have a head gasket problem.....one indicator of this is, overnight, coolant can collect in a cylinder....this will cause the car to start with a slight misfire on initial start up, and then clear up once the coolant is exhausted from the cylinder.....another option is to leave the vehicle pressurized overnight,,,,,next morning remove all spark plugs and then disable fuel and spark(remove injector fuse and disconnect power harness from ICM, the two wire connector on the passenger side)....then have someone crank the engine.....if coolant comes out of a spark plug hole, usually #1, than it's a head gasket or a crack......

The cooling system pressure tester is the way to go, but as a first step I would park the car on level, clean ground (like in the garage) start it and let it run until it reaches maximum temperature and the cooling fans turn on. At this point, the pressure will be the most. I would squeeze the upper radiator host to make sure it is under pressure. Then I would look under it to see if there are any drips coming down, if there are, then I would follow them to their source.

3100's lose coolant because of dex cool. I know this because Ive seen far too many 3100s and 3400s leak because of dexcool. They leak at the lower intake manifold gasket, there is a chemical in dexcool that eats plastic parts, yet they put in a nylon/plastic lower intake manifold gasket. Thanks GM. Also, when dexcool gets old enough, it begins to turn acidic, and eat head gaskets. How do I Know? Experience. You could go the pressure testing route, sure, but with no external leaks, you know its gotta be leaking in the engine. Only place to leak is lower intake manif, and head gasket. Look at your plugs, if they are a lightish pink, or if some plugs have more whitish buildup than others, its probably a head gasket aswell.