There is pretty much only one main place to watch planes at the Kansas City airport, and that is NW Prairie View Rd. which runs directly adjacent to the I-29 freeway on both the north and south sides near exit 15. The west runway (1L/19R) is used most frequently, and when aircraft are approaching to the south (19R) they’ll fly right over this spot. If they are departing to the north they’ll fly directly overhead and either turn to the east or west.
Another spot is a road called NW Hampton Rd which runs through cornfields on the south side of the Kansas City airport. Just take exit 24 from I-435 and go about 1 mile east, and then go north on Hampton Rd for 2.5 miles until it ends at the airport access gate. Traffic approaching from the south will fly directly overhead. A word of caution: local police aren’t too keen on having spotters on this road or even on NW Prairie View Rd. close to the runway centerline. The shoulders are worn from cars constantly pulling over to watch however and there isn’t a lot of car traffic on this road.
One more spot that would give you a good view of landing aircraft is the cell phone waiting lot (see map). To get here, follow the signs on Mexico City Ave. to the economy parking lots. You’ll have to take a ticket because both the free and hourly lots share the same exit lanes but there is no charge for using the cell phone waiting lot for up to two hours. You will be almost directly under the approach path to runway 19L.
As for plane traffic, the dominant airlines at the Kansas City airport are American, Delta and Southwest. There are also a lot of regional jet flights from American Eagle, Delta Connection, and United Express. Alaska Airlines, Allegiant Air, and Frontier also serve Kansas City. The only international flights here are from Toronto on Air Canada. Watching planes is nearly impossible from inside the terminal unless you are flying, and forget the parking garages. The current terminal facilities were built in 1972 and are outdated and cramped, but recent renovations tried to improve conditions for travelers.