Ignoring the alternator replacement Id say without a doubt its a sticking Idle Air Controller.
Does the Idle bounce when its cold in the morning?
With the car off and the headlights on are they a reasonable brightness? Even with the alternator disconnected the car should be able to idle just fine if the battery is okay. The other way around too, if the battery is near dead the car should be able to run when the alternator is providing power (without the headlights, brakelights or rear defrost on).