Hello from Germany,
I am not a beer drinker... but THE beer's countries in Europe are Czech Republic (Budvar and Plzen) and Belgium (with all this various variations)...
If I am buying French or Dutch beer my friends normally "kill" me as I learned that they are allowed to use chemicals in their beer while German beer is only allowed to have natural ingredients inside.
But anyhow some recommended places from North to South:
It's the longest bar of the world - Go to the old town (Altstadt) and you'll find around 1 square miles hundered of pubs etc to test all beer.
The river cruise ships just stop in front of the old town.
UERIGE is a pub which brew his own beer just in the pub.
In Düsseldorf a dark beer called ALT is the local famous style.
Double checked: http://www.uerige.de
2. Köln (Cologne)
Best competitor to Düsseldorf - Same go to the old town and you'll find various brewery pubs around Old Market (Alter Markt).
Berth point same to Düsseldorf.
Their local beer called KÖLSCH and light blond one.
Double checked: http://www.brauhaus-sion.de
Speyer itself has a pub just opposite of the cathedrale to have nice beer in a nice "Biergarten" (beer garden = open air restaurant in the court under trees) with their own brewed beer. I think the pub calls Domhof. Not very sure although I have been frequently there.
Double checked: http://www.domhof.de
4. Heidelberg (from Speyer or Mannheim or maybe direct)
In the old town of Heidelberg just enroute from the Neckar-Bridge (Neue Brücke) towards to the Town Hall on the left side... no idea what was the name but I am taking all international guests to this place because it's very popular and I buy them the beer in big mugs to have a nice souvenir for beer fans from Heidelberg.
Double checked: http://www.brauhaus-vetter.de