Until you have the alternator tested, its difficult to determine if that is the only problem to suspect. I would either take the car to an auto parts store that can test the alternator in the car or pull it and bring the alternator to them. There also may be an electrical rebuilder in your area that specializes in alternator, generator, and electric motor rebuilding. They can be more helpful than the auto parts store personnel when it comes to figuring out a problem.
I would also look into the starter solenoid wiring to make sure a lead has not been placed on a wrong post, and the ignition switch under the dash on the top of the steering column may also be a place to check for miswiring or a bad switch. Finally, if there is any aftermarket audio equipment, lighting, or an alarm/kill switch installed, there may be a power lead that has been miswired somehow.
It is most likely the diodes in the alternator have failed and are allowing current to flow and drain the battery while the ignition is off. You'll know after getting the alternator tested.