Ann Arbor, Michigan has partisan elections for city office. On the evening of July 20, the city council voted down a proposal to let the voters decide if non-partisan elections should replace them. Supporters of non-partisan elections may do a city initiative, however. See this story.
In the 1970’s, the Human Rights Party, which was a ballot-qualified party in Michigan, won several seats on the Ann Arbor city council, but now the council is entirely composed of Democrats.
Councilwoman Jane Lumm was elected last as No Party Affiliation (I.e. Independent), I believe. She was a Republican.