Looks like it's about 50 miles to IAD, 80 to BWI and about 75-80 to DCA (which has the greatest road traffic most of the time). I'd do IAD almost every time if the flight schedules work. Coming from OMA I assume you're connecting in ORD or maybe CLT, so I'd just pick IAD by default. DCA will have the most AA flights but there are AA flights from ORD and CLT to all three metro DC airports.