I disagree with leaving the .243 at home. I have killed multiple deer with a .243
How to hunt the mule deer really depends on the terrain your hunting them in. If your in an open area like Critter described then just like he said, spend a TON of time glassing. Those suckers hide like Superman in a sagebrush flat.
I agree a .243 is a great gun even on big mulies. My dad has shot plenty of whitetails, mulies and blacktail with his.