North Rhine Westphalia would be a good base for both rail and football. Germany has good value Länder tickets, covering all regional trains, trams and underground services (apart from express ICE/IC/EC services) within a given region for between 19-30 per day depending on the state concerned.
Dortmund, Köln, Leverkusen, Düsseldorf, Aachen, Wuppertal and Essen are all in NRW. If you haven't yet experienced the upsidedown railway (wheels are on the roof of the carriage, rail above the carriage) in Wuppertal then you really should! In Essen you've got former DLR vehicles running on the U-bahn. In Köln you have one of the most spectaularly located stations next to the cathedral. Dortmund and Leverkusen obviously are key football grounds.
Aachen is on the Dutch/Belgian border and gives you easy access to those countries on a day trip, and if you go via Eurostar to Brussels you pass through the spectacular new Liege station on the way to Germany.
You can use your Eurostar Brussels ticket to get almost to Aachen - just buy an extension from Welkenraedt to Aachen at Brussels Midi for 5 and use the IC and local trains to get there.
More generally in NRW there's a wide variety of freight and passenger traffic heading north-south, plus the route down the Rhine towards Frankfurt is very scenic. You'll see ICEs of every generation and voltage, Thalys and CNL double-deck sleeping cars, traditional IC and EC loco hauled, plus more red regional trains than you know what to do with.
Stopping off at some Rhine west bank stations at night will not only give you great views of moonlit castles, but you'll see a stream of freight traffic from the North Sea ports to much of central western Europe.
Highly recommended!