What do you mean by self-rule? Singapore is autonomous, but that's definitely not the norm for cities. Almost all of them belong to larger states.
No US city has self-rule even at the level below the federal government. Washington, DC comes closest, but it is technically ruled directly by the federal government (in a manner that is not true for cities that belong to states). China has four "province-level" cities, but is generally accepted to have many more than four cities.