How about volunteering at a no-kill shelter? You could go play with kitties whenever you wanted

The absolute worst part about fostering is the fact that you have to give them up. I cry so bad every single time. I can never get used to the concept of not keeping an animal. It doesn't help when I become too bonded in about 5 minutes flat.

The fact that your apartment doesn't allow pets makes me a little nervous if you were to foster. The main problem is, if they catch you, they have a legal right to remove the animal and you may never see it again