Hm it looks like the thread's title was changed and that makes some of my responses irrelevant as I was dealing, at times, with things that might not be in any city.
I guess one possibility is a woman mayor. At least so far as I can tell New York City not only does not have a woman mayor but it also never had a woman mayor. Seattle had a woman mayor in the 1920s, Bertha Knight Landes, making it the first major US city to do so. Cities not deemed excessively "progressive", or that are even deemed conservative, but that have had women mayors include the following in roughly chronological order
Johnson City, Tennessee: May Ross McDowell in 1961, their first
Phoenix, Arizona: In 1976 Margaret Hance was their first.
Bakersfield, California: In 1981 they had their first with Republican Mary Katherine Jaynes Shell.
Tulsa, Oklahoma: M. Susan Savage was a Democratic mayor of the town in the 1990s.
Colorado Springs, Colorado: Mary Lou Makepeace became their first woman mayor in 1997. I guess she currently works with the Gay & Lesbian Fund for Colorado.
Grand Island, Nebraska: Margaret Hornady is their current mayor.
Grand Island, City of : Mayor
Cody, Wyoming: Nancy Tia Brown is their current mayor.
City Administration (http://www.cityofcody-wy.gov/administration.cfm?id=24 - broken link)
Nashua, New Hampshire: Donnalee Lozeau (Might be a fairly liberal city for all I know, but I think NH is more moderate)
City of Nashua, NH > City Government > Mayor's Office > Mayor's Biography
Major cities that currently have women mayors
Baltimore: Stephanie Rawlings-Blake. Previous mayor was also a woman, but was convicted.
Fresno: Ashley Swearengin, a Republican.
Houston: Annise Parker, also a lesbian.
The small town I live in has had a woman mayor, but it's a small mostly Democratic (albeit Blue Dog leaning at times) town.