Bowless,
Good questions. They are not dumb.
It's been my experience that anywhere there is a motel, there is also a butcher shop/game processor within an hour drive of your motel (60-70 miles).
Wether or not you want the butcher to process your game, they will hang it for you for a small fee in the cooler until you are ready to go home.
The best way to compactly travel with your game is to quarter or 8th (Sometimes you will need to break an elk sized critter down further then quarters to get it to fit in an ice chest) place quarters or pieces of game into an ice chest and put a couple pounds of dry ice in the cooler with your game. If the dry ice melts by the time you get home, just stop at a grocery store along the way and get more dry Ice.
It kind of depends on the price of butchering wether or not I'll have th butcher proccess my meat.
For instance, where I hunt in east Texas, there is a top notch butcher there that is very reasonably priced. If I take a hog, he can have it fully butchered and froze within 24 hours. I still put dry ice with proccessed fair to keep packages froze.
Note: Make sure the butcher gives you back your meat. there are a lot of butchers that weigh you meat and give you processed meat of somebody elses critter. Not very many do this, but becarfull of it none-the-less.
If you are flying, you can put the meat in coolers with dry ice and next day air it home or pay the extra baggage fee and check the cooler.
I feel this is an EXELLENT question. Not very many people figure this cost in when budgeting for a hunt. An elk sized animal, butchered packed and shipped will cost $600-$800. Cut that figure in half with deer/pig sized animals, and double that figure for buffalo/moose sized game.
However, if you want to butcher the animal your self, the hanging fee and dry ice fee is well under $100 bones.
Hopefully some of this will help.
Good luck,
Todd