I know this problem has an old date stamp but the problem is the air doors that direct the air flow to the A/C evaporator or the heater core have lost the foam seal on their sides. This also happens on the defrost/ floor door.
The job to have a auto shop reclaim all the freon in the A/C system and drain the coolant from the engine. Then disconnect the heater hoses and the A/C lines and Expansion valve from the evaporator. Then the time consuming fix this is to remove the dash and the heater/A/C unit and open it to reveal the doors. You can replace the seal by first cleaning off all that remains of the old seals and cutting out need seals from dinner plate protector sleeves found in moving departments of hardware stores. Cut it to the right size so the doors is sealed but not prevented from moving or sealing due to the new seal size. Using 3M spray tack, spray on one side of the new seal and after masking off the metal door, the one side of each door at a time with an even light coat. Let it dry 3 to 5 minutes and put the seal in place with "one shot" placement.
The age of car I would recommend that the heater core be replaced at the same time.
The car is worth it if it isn't rusted out. I have done several including to of mine. An auto shop will charge for 12+ hours of labor but a friend who likes to work on challenges could handle all but reclaiming of the freon.
Parts cost is less than $30.00 provided your anti-freeze is good and nothing gets broken.
Some good background music and a few cups of coffee always help the job go better!