Leverkusen: travel
Cologne Bonn Airport is the closest for Leverkusen. You could reach Leverkusen from the airport with one change of train (at Koln Messe Deutz) in as little as 40 minutes.
Dussledorf Airport is a pretty good second option. Trains do run directly from the airport through Leverkusen Schelbusch station - and if it doesn't stop there, just head on in to central Cologne and make the short 15 minute journey back out again.
If you are staying in Cologne and visiting Leverkusen, make sure any day ticket you buy must be a 2b City Plus ticket as Leverkusen is just outside the inner limits.
A Koln card DOES include the journey to Leverkusen and back within its free transport (as well as to and from Cologne/Bonn airport).

