FWIW 2000 Regal SC 3800, although this applies to all 3800's.
Pulling into a friends driveway the other night the car makes an interesting sound. Like a wobbling pulley on the belt path. It's a learned sound, once you know it..you know it. Pull in, turn the car off and see a little fog/mist/smoke from under the hood. Temps etc were fine the entire drive.
Lifted the hood and looked around. Belts have some coolant on them. Some is on the radiator in line with the belts. The crank/harmonic balancer are wet.
I looked to the coolant elbows and they were dry, ruled out.
I looked at the radiator wondering if it went and the coolant went onto the belts, it wasn't overly wet. Doubt it's the issue.
I looked at the motor. HB/crank and front of timing cover are wet. Belts are wet. Coolant appears to have been slung around by the belts. Most likely a water pump.
Loosened the radiator car once it cooled. The system was full. Drove home (short drive) and kept an eye on the temp.
Once home (actually next day) I dug into it.
Pulled the belts off and ran my finger under the water pump. It came back wet. Good indication it's likely the pump, Removed the water pump pulley and got my finger closer to the weep hole of the pump. Definately wet. Also letting it sit overnight, the puddle was under the motor, not the radiatoor. Radiator was ruled out at that point. I pulled the pump off and spun it. Squeak, rattle.. crunch. Pump didn't have excessive play. But the bearings were bad and likely caused the leak.
Cleaned the surface, pulled a spare pump out of the part pile, cleaned it and tossed it on with a fresh gasket. Filled the system and then started it up. Ran the car with the cap off up to the thermostat temp to allow all the air out. Topped it off and capped it. Slightly overfilled the overfill jug in case any air remained.
$14 for a gallon of coolant was my cost since I had pumps and gaskets on hand.