Paragon City has a Mayor, and they are a fictionally a part of the State of Rhode Island. Assuming the fictional world's government structure matches that of the real world, they would also likely have a city council. In fact, there are numerous missions scattered throughout the Hero side that requires saving city councilors.
As for who their current Mayor is, that remains to be seen. In 2005, it was Mayor Morales. The Mayor of Paragon City during the early 20th Century, was Michael James "Spanky" Rabinowitz, who maintained control of the city’s politics for nearly thirty years. Other parts of the in-game like Croatoa, have their own Mayor.