Hunter College is one of the best center city schools. It is located in the heart of the East Side of Manhattan and is very close to Central Park, Metropolitian Museum of Art and great shopping (for any budgets).
The best thing is the subway stop at the school, this opens the whole city to you. The art department is sceond to none and the professors really care about your progress. The only not so good thing about Hunter is the lack of green space to sit and relax in, but Central Park is only four blocks away.
This was a top-rated college when I attended from 1964 to 1967. Because it was free, students were required to have a 87% high school average, and a very high rating on SAT's. It was a great opportunity for poor students, most of us the children of immigrants, to become upwardly mobile. As a whole, it was a wonderful experience.
I don't know the state of Hunter today, and can't say if I would recommend it. I do know that the City University is no longer free.