Leverkusen: the city
No, it's not a suburb of Cologne, even though it looks like that on a map. Leverkusen is a city in its own right, with green space between it and Cologne - albeit all of a mile or so.
Leverkusen is a relatively new city, created in 1930 through the merger of several places. It's known throughout Germany and the world as a chemicals base, home to the Bayer company which created the football club.
It'll come as no surprise that its biggest landmark is related to the company - the huge Bayer illuminated sign is apparently the biggest neon illumination in the world. Pub bore fact.

That's one big sign: The Bayer illumination.
Other than that, and without be too harsh, Leverkusen is unlikely to detain you long. It's a working city, not a tourist destination.
You could stay there - there are a few hotels in town, mainly for the benefit of visiting business people - but its close proximity to party city Cologne means that remains a far more popular option.
As prices in Cologne can rocket during trade fair I stayed briefly in Hotel Astor in Opladen, a district of Leverkusen. Pictured here on one of main drags in Opladen, it's a good option at a cheaper price.
It's too far to walk from there to the ground, but free football buses run from Opladen bus station to the Bay Arena (leaving at 2pm on 3.30pm Saturday matchdays).
Alternatively you can catch the train and go one stop down to Leverkusen Schelbusch.

