someone has already registered all county.uk domains in 2019 :(

Virginia cities are independent, not within counties. And there's both a Fairfax City and Fairfax County. Making things even more confusing, the county seat is Fairfax City despite the city not being part of the county. The county has fairfaxcounty.gov while the city has fairfaxva.gov.

There are a handful of other independent cities in the US, but the vast majority are in Virginia.

Look-alike Unicode characters.

There's also the edge case of the (unofficial) 6th borough of NYC: https://en.wikipedia.org/wiki/Sixth_borough

ny.ny.us

  New York City is a place so nice
  Everybody says it so they had to name it twice
  New York my happy love's you
  (I love you very much)
  I could not live without you
  So let's always keep in touch

https://www.youtube.com/watch?v=82f7BB6zNOc

For city.state.us, I'm pretty sure first to file (while filing was available) wins...

Ohio doesn't (or at least historically didn't) have a highlander restriction for incorporated cities.

Oakwood, Cuyahoga County was incorporated in 1951 although Oakwood, Montgomery County was incorporated in 1908. There's also an Oakwood in Paulding County, but its wikipedia page doesn't have an incorporation date or explicitly declare it incorporated or not. I thought there was a famous Ohio city with a same named city elsewhere, but I must have been thinking of somewhere else. I will note that Pennsylvania has an awful lot of same named Townships.

City name in the US ends up being a pretty wild concept when you dig into the details. Often what people are using as a 'city name' is really the name of their post office which statistically has a high correlation with the city they live in. But of course, lots of people live outside incorporated cities, and postal boundaries are independent of political boundaries.