Which of the 50 United States has the most cities and towns?

It might be Texas:
"The Texas Cities section of the gazetteer has profiles for 9,197 populated places including cities, towns, neighborhoods, subdivisions and settlements."

http://texas.hometownlocator.com/cities/

California, although it has a greater population than Texas, has not so many towns and cities:
"The California Cities section of the gazetteer has profiles for 6,441 populated places including cities, towns, neighborhoods, subdivisions and settlements."

http://california.hometownlocator.com/cities/