Is there something special about "City Universities" and do the municipalities somehow govern them? There are several universities with the title "City University". Is there something special about them, is it some kind of special model of founding, governing and developing the university by the local municipality/city/greater-city?

I am participating in the political party/movement and I see the need for some kind of focused higher education institution in our city for some demographics that is neglected by the central government and so - I have feeling that we can propose to establish our own city university to boost education in this special demographics. But are there "role models" for universities that are founded by the cities in the recent half-century?
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.