Can I get married at the City Hall on a Sunday?

Chances are no because most City Halls are closed on Sunday.

Where you can get your marriage license in Cook County

Vital Records

And no, Marriage at government offices are done only at specific times M-F, and the culturial center on Saturdays.

Judges can be hired ( as a pastor can) to do onsite weddings or weddings outside of business hires.
Many pastors will do very low cost weddings on location or in their home or yours.