I go tent camping several times a year and I HATE messing with ice to keep food cold. So I was wondering: Is there a way to keep cheese good for about a week without refrigeration? Or maybe a certain type of cheese that would work.
As long as it is not too hot, most REAL cheeses can keep at room temp for a few days fairly easily. Same with eggs and butter. The easiest ones to deal with would be hard cheeses. Some really can last weeks without refrigeration. About 55 deg. F is optimal, and the temp artisan cheeses are aged at.
When I used to take 1+week long canoing trips in Northern Canada we took the individually wrapped string cheese. It usually is marketed for kids as snack items but since it was sealed in individual plastic cylinders it kept for at least the week we were out canoing (summer).
Try the plastic and wax wrapped Baby Bells, that you can find at most grocers. They hold up quite well. As has also been stated upthread, hard cheeses do well. Also most wax wrapped cheddars will do OK for a few days, unless it's really hot outside.
I backpack a bit and I do sometimes take cheese with me. I can only comment on what I do and know, there is however, more info floating on the web.
Sharp cheddar last longer than mild cheddar. Hard cheeses last longer than soft cheeses. I personally prefer mild, but for a trip I take sharp cheddar. For a camping trip I'm not really interested in other types of cheese so there you have it. I've heard it said that you should wrap the cheese in cheese cloth to keep it. I personally just grab a small brick at the store and throw it in my bag. Once I open it I wrap it up in a butchers paper. I try to be particularly careful on handling the cheese that I'll eat later, I've read that if oils on you hands get on to the cheese it's more likely to get black spots etc. in the up coming days. I've also read that once the cheese is open not to store it in a non breathable plastic bag or what not as this could build up humidity in the container with bad results.
Regardless of these tips, if your cheese does get small black spots just cut them off the cheese is fine.
Once cheese gets warm it starts feeling soft and slimy. This is normal and is still OK.
Hope this helps.