Most cheeses will handle a number of days out-though the harder it is, the better the storage. So hence, go for real cheese, not processed junk. Cheddar, Swiss, Sharp cheddar, Parmesan and it's cousins, etc-lots of choices!
It does get soft after awhile, but it is still edible.
One rule to watch is this: handle the cheese as little as you can. Your grimy mitts will do more to it than not being kept cold! ;-)
Also, you can cut cheese at home, and dip it in paraffin in serving size chunks. Helps keep it fresher. Just peel off the paraffin when you are ready to use it! (for instance, 1 ounce is about right)