Oslo vs the rest of Norway
Does not count. Nobody likes capitals (Paris vs. rest of France, Rome vs. rest of Italy, Athens vs. rest of Greece etc.), while the capitals don't care.
What about Bergen-Trondheim?
New York is above considering any American city its worthy rival.
Even not L.A.? Otherwise, I suggest for the purpose of this thread to declare NYC the unofficial capital of the USA, which means it is out...
Memphis v Nashville. Same state, different worlds. Memphis is ghetto Deep South blues. Nashville is white trash Country rhinestones. They're growing way faster and they can have it. I don't want to be the next Atlanta. We're in the Goldilocks zone for size, as far as I'm concerned.
That sounds interesting, and thrills the musician in me. Tell us more! Do you have "Nashville jokes" in Memphis? Band battles? Competing events aside from sports (like the Cologne-Düsseldorf carnival rivalry)? Does the rivalry reflect on state politics?
Stephenville vs. Brownwood
Midland v Odessa
Texas City v Lamarque
I must confess I am neither familiar with Stephenville, nor Brownwood, nor Texas City, nor Lamarque. Nevertheless, Midland-Odessa sounds quite interesting and makes me curious about more details.
A few more cases that caught my attention and interest, because they were new to me, and/or might provide interesting case studies:
Alberta-Edmonton
Rochester vs. Buffalo
St. Louis vs. Kansas City
Philadelphia vs. Pittsburgh
Cleveland vs. Cincinnati
Houston vs. Dallas
Seattle vs. Portland
.. and of course
Karlsruhe/Mannheim (first time I have ever heard of it)