Is there something special about "City Universities" and do the municipalities somehow govern them?
In general, such schools don't necessarily have that close connection to the city government. The obvious example would be City University of New York. In that case, it was founded by the state government. Seven of the trustees are appointed by the governor of the state of New York , and five by the mayor of New York City. But all of those are with approval of the senate, which is a state level office. See https://en.wikipedia.org/wiki/City_University_of_New_York#Management_structure .

On the other hand, the equivalent in London has a closer connection to the City of London (which itself is a complicated entity). https://en.wikipedia.org/wiki/City,_University_of_London 

I'm not aware of a specific city-centric model of the sort you want, and a lot of these seem to be developed on a case-by-case basis. Your best bet may be simply looking through a lot of these and seeing how they handle governance and other related issues and looking for what best meets your needs.