Good Luck, some HOA'S refuse to let them in to some single family developments. And as far as apartments go I would think it would be even harder. I suggest you ask for the HOA rules and regulations where ever you go, read them carefully before signing any lease agreement. They should have a list on what dogs are acceptable and the one not permitted or accepted. Remember its your responsibility to read the rules provided, if you sneak in you can be evicted.
Personally I think the poor dog's get a bad rap because of bad owner.
The Best to you,