Okay, with that in mind, I would have you coming into Dallas on the afternoon of the 9th. I would hit the Lester Lorch courses on the way in as others have recommended.
Lester Lorch - Coyote - Lester Lorch - Beaver
That is a Saturday, and there would be plenty of nightlife to go hit if you aren't too tired. I'd recommend a motel up in North Dallas or the near north-northeast suburbs (Garland, Addison, Plano). On your full day in Dallas, hit Harry Myers and maybe Towne Lake up in McKinney.
Leaving the next morning for Oklahoma, I'd hit Lake Lewisville on the way out of town.
When you get near OKC, I would pull off I-35 in Norman and hit Griffin Park and then stop in OKC for the night. The Bricktown District downtown is kind of neat. There's a good hub of motels and eateries out at I-40 and Meridian. If you have time for another course the next morning, I'd recommend Dolese Youth Park up towards the NW part of the city.
Heading up to Wichita, there's pretty much nothing spectacular in between without deviating from the interstate much. There is a very nice private two course complex called The Lodge in Pawhuska, OK, which hosted a NT last year, but this is in the boonies almost 1.5 hours off I-35.
In Wichita, you could almost do a coin flip between Herman Hill Park and Oak Park. Oak is a pretty park and has more water threat, but Herman is more dynamic because it has movable pins. Its also probably the easier of the two to find as it is at a major intersection. There's some budgetary lodging just blocks from Herman, but unless you want to potentially deal with something like this during the night, I'd steer clear of them. I'd in fact avoid any lodging with the word "Broadway" in the address. There are plenty of motels along US-54, and I'd recommend one east of downtown as some on the west side are getting ghettoish in their own right. It'll also get you on your way quicker.
On the way to KC, stop in Emporia, Kansas and play at least one of the Jones Park courses. The east course is the more challenging of the two.
Oh, I forgot to mention I-35 is a toll road from just north of the OK state line to Emporia. Have about $6 ready for this ripoff.
Going into KC, Prairie Center Park in Olathe is a decent play, but not the best in town. I would head into downtown and stop at Disc Golf World as jartiv recommended. Its in an arts district on the east side of downtown. The showroom is a bit on the small and spartan side, but if its not up front, they might have what you're looking for in the back. If you still have time for a course, hit either the amazing Water Works Park or Cliff Drive. If you're up to it, there's also KC's famed 11,000' monster at Blue Valley Park. I would plan at least 3-4 hours to get through Blue Valley. Both it and Cliff are in less than decent parts of town so make sure you lock your car and don't leave anything in view that might be tempting to steal like your GPS.
On the way to St. Louis, Columbia, MO has some decent courses, but I would pass on them to get to suburban St. Louis and play Sioux Passage.
Hope that was of help. I also hope the snow melts in some of these places before you get there. Have a safe trip.
