Brett, It's a no brainer on Monterey V. Chicago. Monterey is the states Kingdom of golf. Fog, wind, and the Marine layer provide for a variety of weather conditions. Even if you balk at the cost of the Pebble Beach Co.'s rates, you can play Pacific Grove daily, on top of Pebble Beach, Spyglass Hilll, Spanish Bay, Poppy Hills and the Fort Ord courses, Black Horse and Bayonet. Even the poorer quality courses are special on the peninsula. ( Monterey Pines )
The idea of driving across country is a fantastic one, if you have the time. But, with the resources available to you through the generosity of people on this site, you may want to save that time for golf courses.
There is an interesting dynamic happening out here in Nebraska concerning the State Patrol. Due to the price of gas, and short falls in revenue, the attorney general has focused the state patrol officers, close to the bigger towns. They've been writing tickets like crazy, but mostly in town. So the extreme rural parts of your trip (SH and Prairie Club) should be clear sailing.