hmm...i was gonna say boarding house, but i'll have to go with a verison of the seasonal theory, one based on their work schedule. i think of them as forming a repertory company kinda parallel to the one made up of their muppeteers--there are some close pairs/groups who see each other in their spare time or get together for parties, but they all live in different places and have different lives (i can imagine gonzo hanging with the type of wierdos that fluster kermit on set and that he would probably try to avoid in his social life).
that said, they spend most of their time at work anyway, in the theater and the tour bus. and whenever they're doing a project/adventure, they click as a group both on stage and in the wings, so it probably feels natural when they're forced to share bathrooms or trip over each other in dressing rooms--they end up functioning like a family, both aggravating each other and caring for each other. so i would say the apartments are the least likely--who lives next door to all their friends or colleagues? and the boarding house is akin to the theater, hotel, lockers, etc, as their chill space in the studio for the little down time they get while they're working so hard to be zany and weird.