In general, Joker actually isn't the kind of guy who'll take a stranger back to his place of residence, at least not straightaway. When you have literally countless thousands of people who actively want you dead, it pays to take a few very minor precautions before welcoming someone into your actual abode.

But he's not in Gotham anymore, and, more importantly: the stranger in question in this particular scenario can teleport and heal, and who knows what else, besides?

"A grand idea." Joker beams. "We could order up some munchies, even. Least I can do is get you a meal, after all of that..." He glances around, trying to figure out where, exactly, they've wound up. "The apartments where they stick all the new folks. Those are... what, thataway?"