Our 66 Coupe (289-2V, auto, pwr steering/brakes, after market security alarm) keeps running down the battery, overnight.  Auto Zone tested it; first-found the battery was bad (bought a new one), second-checked alternator, charging okay, third-found that the voltage regulator was bad (replaced with a new one from NAPA); each time, the next day the battery was dead and car had to be jump started.  Can anyone tell me where to start/what procedures/tests to run (with a multimeter?) to find the electrical drain/short/or?  Thanks.  

I am no electrician, but I might help you isolate the problem.  First, you want to make sure that no lights are left on such as the glove box or interior. I am no electrician but you want to split the electric wiring in half to find out if the drain is coming from the engine compartment, or from the dash, or from the rear.  To the left and up from your Master Cylinder is a wiring plug.  Pull that out and let the car sit overnight with a full battery charge.  Plug that back in and if the car starts the next moring, the the short is not in the engine compartment.  If you take the kick panel off the driver's side, you will see the connections for the rear part of the car.  Unplug them and repeat the same thing.  If the car starts the next day, then you now know where the short is.  If it doesn't, then your brake lights have been on all night.  Yeah, mine started sticking a few months ago, and that was my problem.  Hit the brake switch attached to the brake pedal with some WD-40 or get a new switch. If that ain't it, it's under the dash.  Do you enjoy lying on your back with a multi-meter?  I didn't think so.  But, that is what you are going to have to do.  Take the gauge pod out, get yourself a good wiring diagram and start testing.  

I think you can disconnect the battery cable and put a test light between the cable and battery post and then follow the isolating procedures that soaring3 mentioned above. That way you won't have to wait until the next day to see if the battery drains.
Unless I'm mistaken (and occasionally I am) the test light won't light up unless there's a draw on the system. If everything is off it shouldn't light up.
Someone please correct me if I'm wrong.  

Good advice from the other two posters. I'll jump in too.  If the battery goes dead overnight thats a pretty good drain and suggests that it's either a short or a light bulb on all the time, Glove boxes and trunks are good places to look. take a walk around the car when dark to see if you can spot any lights that are on that shouldn't be.  With that completed, the best way to find this is with an ammeter that can read at least 25 amps hooked in series with the battery cables (either one is ok, I prefer to use the neg terminal) Determine if you havea drain greater than .500 milli-amps, (If below .5A, the problem is in the battery and it should be returned for a comprehensive load test).

I would expect to see 10 amps or higher based on your data. Go to the plug that Soaring described and unplug it, if the amperage drops the circuit in question goes into the interior of the car. You'll need a wiring diagram to troubleshoot also. From there it's just a matter of isolation by removing the fuses one by one until the load drops. That's the affected circuit.