There are rivalry games in NCAA football between regional teams who aren't conference affliated. So why not do that in the NFL?
I know, I know ... the NFL has a pretty sweet scheduling system now and yada, yada, yada. I agree with you that the logistics would kinda suck. But let's do it just for fun:
Redskins-Ravens: You gotta have the battle of the Beltway.
Giants-Jets: Maybe they could play for a Big Apple Trophy or something.
Cowboys-Texans: Two franchise who share the same state and little else.
Eagles-Steelers: We can call this the STEAGLES GAME after their brief merger during WWII
Buccaneers-Jaguars: Jags get the nod over the Dolphins because of the northern Florida thing. Can we get them to play in Orlando?
Rams-Chiefs: Show Me a better game!
Niners-Raiders: The Bay Area Classic may one day actually be one.
Cardinals-Chargers: The two Southwestern teams get to tangle.
Bears-Colts: Not just because of the whole Super Bowl XLI thing, though it helps.
Panthers-Titans: As I drive through the Great Smokies, I get to hear both Carolina and Tennessee games on the radio. That's all I got.
Lions-Browns: It could be a bit catchy.
Falcons-Dolphins: The Second Biggest Outdoor Cocktail Party, this is not.
Seahawks-Broncos: Okay, not much here ... but someones gotta join these two pieces together
All that leaves the Packers, Saints, Vikings, Patriots, Bills and Bengals as outsiders. So ... let's just do this:
Packers-Patriots: Packers represent the old time greatness of a franchise; the Patriots represent the nu skool of that.
Saints-Bengals: If you think about it, it does make sense. Both are the laughingstock of their conferences over the past two decades. And they can have fights over WHO DEY and WHO DAT.
Vikings-Bills: Um ... and there you have it!