If I'm getting a pizza, but don't have a fridge to store the leftovers, what's the best way to go about it?
If you get a Chicago-style deep-dish pizza with some toppings, especially onion, the likelihood that it'll start growing mold within a couple of days without a fridge is quite high. Mold likes moisture, and onion is especially good at attracting mold (mushroom is itself the mold already).
If you get a New-York-style thin crust cheese-only pizza, and keep it in the original carton box (don't use plastic!), it'll likely dry out within a couple of days, and then it'll probably be good for weeks, if stored in a well ventilated environment (e.g., in the pizza carton box). The trick is that cheese itself has a lot of good bacteria, and it'll be a while before the bad mold bacteria starts growing in, especially if it's all dry and not moist. The dry slices would be more alike crackers, though, but would be great as snacks!