Hi Susan,
I have a leaky 83 as well. In fact, I'll be checking and caulking the firewall penetrations tomorrow.

If none of the drain points are apparent when you first look, you might try giving them something to drain. In the process of looking for leaks, I poured water all over the area at the base of the windshield. Much of it went into the fresh air vent and came out of drains just behind the front wheels, from the indent in the seam (opening faces down, about 1" long, 1/4" wide) that another poster mentioned.
Once you see where these drains are, you will find more if you follow this weld seam towards the rear wheels.

It seemed to me to make sense to pour lots of water through as I poked at the drains to clear blockages. You might also want to repeat with the car facing up a slight incline to clear the rear drains.

If you pour the water in too fast you may also succeed in testing the drain for the heater housing / A/C evaporator. This drain passes through the transmission hump, roughly even with the dashboard, centered under the car. Don't use the wire-poking method to clear though, as the rubber hose feeding this drain takes a sharp bend a couple of inches in (that's where the clog would likely be, if any.) To get at this hose you need to remove the passenger side cover of the center console and look for a small hose dropping from the heater/blower housing down to the floor.

During all of this pouring of water in and clearing drains, you should watch to see that water is not collecting in any of the footwells (with carpet and foam pad pushed out of the way), and that none of the plastic plugs (about 4" diameter, milky colored) that were mentioned in other posts are leaking. If water is collecting, the drains aren't draining or the plugs aren't plugging.

Good luck and try to reduce the leaks before your floor rusts as much as mine.
Joe