A great all around cartridge, if you already have a .30-06, would be a .243win. A bit lighter than the 30cal, the .243win is a lil nicer on smaller game like coyotes (not as nice as that .22-250 would be), but still able to handle deer sized game, and Elk with the proper bullet, well placed. The more I hunt whitetails, the more I start to consider the .243win the optimum whitetail cartridge, and it's fantastic for reaching out and knocking down coyotes at long ranges.

EDIT: But, if you don't have a 22caliber centerfire, and you DO have a .30-06, I'd probably be looking at a 223rem or .22-250 over the .243win first, then think about bridging the gap later. The .243win will be a better all around cartridge, but since you have a deer rifle, you don't really need another, so I'd lean towards a dedicated small game rifle. Great excuse to pick up that .22-250.