Tulsa.
The halfway point between Tulsa, Oklahoma, and Vicksburg, Mississippi, is Conway, Arkansas, if you're going via Fort Smith, Little Rock, and Pine Bluff.
Philladaliphia
Chicago, Illinois and Atlanta, Georgia are 719 miles apart. A city located halfway between them would be Bonnieville in Kentucky.
Kalamazoo
The city of Anchorage in Alaska is roughly halfway between Sydney and Chicago, in terms of distance. However, since there are no direct flights between Sydney and Anchorage, it may not be the most practical midpoint for travel purposes.
The exact halfway point is the corner of Ecorse Road and Middlebelt, but that is on a straight line between Wyandotte and Canton.
Atlanta
Elk City, OK
bum
Ragsdale, Arkansas.
If you go south to Denver and cut across, the halfway point is Collyer, KS. If you go west to Kearney and turn south, the halfway point is Smith Center KS, which is about 15 miles away from the center of the contiguous US. There's a plaque there.