It's not the drain or the heater core. More than likely, your cowl has filled up with water, and it's spilling over the HVAC intake and ending up in your passenger footwell. Remove your wipers, and then the wiper cowl covers. To the far right (passenger side), there is a drain hole that is likely clogged up. Unclog it (usually it's leaves that does this), and you should be golden.
This same thing happened to my when I had my 89 Taurus GL, only it happened during a torrential (like 3" of rain in a hour torrential

) rain storm, and in the morning I went down to my car only to find 4" or so of standing water on the passenger side of the car. Fun times.