Assuming you haven't made hotel reservations, etc. this is one local's opinion on what you should do.

Kauffman Stadium is a beautiful ballpark...in a sea of parking lots, adjacent to two freeways. As mentioned previously, there are two hotels within walking distance of Kauffman Stadium, but...I've never heard anyone have any comment on them than "they're the ones by the stadiums" :-)

If I were you, I'd stay at a hotel downtown (anywhere in downtown proper, or the Crossroads or Crown Center districts), as there's much more to see/do nearby than by staying out by the stadium. Bus fare in KC is $1.50/trip, $3/day pass, and there are bus routes between the airport and downtown - 229 - and between downtown and the stadiums - 47. However...the trip times are about twice as long as it would take to drive those distances, and both routes only run hourly for large portions of the day. Given that, you may want to consider taxi/rideshare, looking at any hotel/third-party shuttle services, or renting a car for some of your getting around needs. Within downtown, there is a free streetcar as well.

Regardless what you do, enjoy your time in KC!