Depending on what kind of food you like, the Plaza is probably the best place to head for a good lunch. Only downside is that you really will only have about 2 1/2 hours to spend there, considering the time it takes to rent a car, drive down & back, return the car, and get back to your gate by 2:30 or so.

The River Market idea would give you more time because it's right downtown, and about 15 minutes each way closer to MCI than the Plaza. Saturdays would be a good time to visit the outdoor market, the Steamboat Arabia museum (right next to the market), and still have time for lunch at one of the restaurants there. There's a nice microbrewery there, a good Italian joint, as well as 3-4 other restaurants.

If you like to gamble, you could hit one of the boats. Harrah's and Ameristar are the two "classier" boats (although none of them are terribly upscale). Argosy is a few minutes closer to the airport; it's a little more low-rent, and has slightly looser slots and slightly friendlier table rules. Argosy occasionally lets you play 10x craps, something Harrah's and Ameristar never seem to do. KC's fourth riverboat, the Isle of Capri, is downright scary IMHO.

For transportation, a rental car is about your only choice if you aren't going to a major hotel. I've rented literally hundreds of cars at this airport (which is a scary fact in and of itself), and have found Hertz to be the fastest and most reliable, provided you have a #1 Club Gold card of course. I'd consider National a close second in terms of number of shuttle buses and speed of getting/returning a car. This rental shouldn't cost you more than $20 + tax for a small car.