Explorer's is great (8050 Wornall Rd.). Lots of toys to play with and the owner, Wes, has a huge collection of vintage drums.
The 18th & Vine area is ok, it's kind of overdone and fake, but the Blue Room (the jazz club that's part of The American Jazz Museum) has some good jazz. Depending on the night, however, there might be some not-as-good R&B/smooth jazz nonsense.
The other two good jazz clubs are Jardine's (4536 Main St.) and the Phoenix (8th & Central). Again, they're hit and miss as far as what kind of "jazz" your going to hear on a given night.
I'll be playing at Jardine's on Saturday the 27th from 10:30 pm to 1:30 am with a great singer named Shay Estes. Come say hi!
Also, it would be a cryin' shame if you came all the way to Kansas City and didn't have some BBQ. You want to hit Arthur Bryant's, Gates, and/or Oklahoma Joe's.