Republicans don't pick cities to run, voters pick people to run their cities. Every election we have a Democrat and Republican candidate for the city and county seats. The people overwhelmingly vote Democrat every election. It has nothing to do with Republicans don't know how to run big cities, it's that voters don't know how to Fn vote, just like this past election.
Maybe you heard of a guy by the name of Senator Voinovich. He's a old timer. He was the last Republican Mayor of Cleveland, and when he ran things, the city did great. He also spent two terms as Governor and again, things were fine. He ended up in the Senate and that's where he passed away many years ago. Or look at NYC. When Rudy got in there the place was in shambles. The mob ran a lot of the city, crime was worse than it is today, windshield washing bums ruled the main streets. If you didn't pay them after they washed your windshield, they'd bust the damn thing out of your car, homeless people everywhere you looked.
Rudy got in there and cleaned it all up. Ran the mob out of the city, got rid of the bad cops and replaced them with good cops, got the homeless people off the streets, and violent crime decreased rapidly.
So it's not that Republicans don't know how to run a big city. They know way better how to run them than any Democrat. It's that Republicans seldom get elected in those big cities and the people are not smart enough to realize how they vote isn't working, and it's time for something different.