Every place entails some sacrifice of either convenience, quality of golf, or cost/access.
For ease and convenience, you can't do better than Dallas: stay at TPC Las Colinas, play there, Dallas National, Colonial, Brook Hollow.
For quality of golf and accommodations and relative ease, Reynolds Plantation 75 miles east of Atlanta.
For a surprise choice that gives you ease of national access plus great golf, I'd actually consider Chattanooga, which is drivable from Atlanta as well as accessible, and you have Honors Course, Lookout Mountain and Black Creek.
Phoenix is actually very easy to get from everywhere within 4 hours and has unlimited great golf.
St. Louis is the most central, but golf is really a problem there.
Chicago conjures up way too much traffic and spent spent getting around.