Bars

Schwadbud
Big club-run bar at the stadium itself (Bismarckstraße 122-124). Seating for 250. 24 screens. Sports bar / club museum design and feel. Opens two hours before kick-off on matchdays. Match ticket required to get in. Closes two hours after the game, unless they're showing a later match on TV (weekends only). Snack food available (sausages, etc.).
 

Stadioneck Leverkusen 
At Karl-Marx-Straße 36, 51373 Leverkusen, a 6-minute walk from the ground. Said to be THE pre-match meeting point for many fans. Relatively small corner pub, with standing room outside in good weather. Off-licence next door. Grilled sausages etc. available to eat. Away team colours not welcome. Cash only. Google reviews here. 

BAX Biergarten 
At Leverkusen Bismarckstraße 127, 51373 Leverkusen, directly opposite the ground. Space for up to 400 people in the beer garden. All games shown live (but apparently only on small screens). Was previously the 'Pille' sports bar. Now with a Bavarian beer garden theme. Website here (German only). Google reviews here. 

 

Restaurants:

Haus am Park
Just down the road from the BayArena at 186 Bismarckstraße, this modern restaurant offers German and Central European cuisine. Google reviews here.

Mille Lire
Italian restaurant (including pizza) close to Leverkusen Mitte station (at 5 Friedrich-Ebert-Platz). Highly rated on Tripadvisor, as seen by the English reviews here.

Zagreb
European/Croatian steakhouse, also on Friedrich-Ebert-Platz close to the station (no. 124). Tripadvisor reviews in English here.