Question: What age is the minimum for running for mayor?

Age of candidacy laws in the United States

This article delineates the age of candidacy laws of the federal government and individual states of the United States.
Federal government
President of the United States and Vice President of the United States: 35 (Article II, Section 1, Clause 5 of the United States Constitution)
United States Senator: 30 (Article I, Section 3, Clause 3 of the United States Constitution)
United States Representative: 25 (Article I, Section 2, Clause 2 of the United States Constitution)
State government

* Qualified elector/registered voter requirement.

† State Senate membership requirement.

N.A. implies that such a position does not exist in that state.
Alaska
Any public office: at least 18 (qualified voter requirement)[18]
Arizona
Any public officer: at least 18[19]
California
Mayor: at least 18 (qualified voter requirement)[20]
Colorado
Any public office: at least 18[21]
Connecticut
Municipal officer: at least 18 (qualified voter requirement)[22]
Georgia
Any public office: at least 18 (qualified voter requirement)[23]
Hawaii
Neighborhood Board Member: 18
Idaho
Mayor: at least 18 (qualified voter requirement)[24]
Illinois
Comptroller: 25[1]
School Board Member: 18 (qualified voter requirement)[25]
Indiana
Mayor: 18 (qualified voter requirement)[26]
Iowa
Any elected office: 18 (qualified voter requirement)[27]
Louisiana
Treasurer: 25
School Board Member: 18
Maryland
Circuit Court Judge: 30[3]
County Sheriff: 25[3]
Other county offices: vary according to local law[3]
Any public office: at least 18 (qualified voter requirement)[28]
Massachusetts
Most offices: 18
Michigan
State Court Justice: less than 70[29]
Any county or local office: 18
Minnesota
Many offices: 21[30]
Montana
Mayor: at least 21[31]
Nebraska
Mayor: at least 18[32]
Nevada
Any public office: 18 (qualified voter requirement)[33]
New Mexico
Most offices: 18 (qualified elector requirement)[34]
New York
Comptroller: 30[8]
North Carolina
Many offices: 21[11]
Municipal offices: 18 (qualified voter requirement) [35]
North Dakota
Mayor/council: 18 (qualified voter requirement)[36]
Oklahoma
State, county, and municipal public offices: at least 18 (qualified voter requirement)[37]
Oregon
Sheriff: 21
Other county and local offices: 18[38]
Justice of the Peace: 18
Pennsylvania
Mayors of Third-Class Cities: 18[39]
Rhode Island
Any elected office: 18 (qualified voter requirement)[40]
South Carolina
Judicial: 32[41]
South Dakota
Public Utilities Commissioner: 25
Mayor/alderman: at least 18 (qualified voter requirement)[42]
Tennessee
Supreme Court Judge: 35
Other state judges: 30
County mayor/county executive: 30
Sheriff: 25
Constable: 21
County School Board Member: 18 (registered voter requirement)
Texas
Comptroller: None
Any public office: at least 18 (qualified voter requirement) [43]
Vermont
Town officials: at least 11 (qualified voter requirement)[44]
Virginia
Any office: at least 18 (qualified voter requirement)[45]
Washington
Any office: at least 18 (qualified voter requirement)[46]
Wisconsin
Any city office: at least 18 (qualified voter requirement)[47]
Wyoming
Any municipal office: at least 18 (qualified voter requirement)[48]
Local government
Many states require elected municipal officers to be at least 18 years of age or be a registered voter in the city thereof. Montana requires mayors to be at least 21 years of age.
As of November 2016, most U.S. cities with populations exceeding 200,000 required their mayor to be a registered voter in the city thereof or at least 18 years of age. Here are the following exceptions:
30 Years: Denver, CO; Honolulu, HI; Memphis, TN; Nashville, TN; St. Louis, MO
25 Years: Baltimore, MD; Colorado Springs, CO; Columbus, GA; Glendale, AZ; Kansas City, MO; Omaha, NE; Philadelphia, PA; Washington, DC Westminster, MD
21 Years: Louisville, KY, Oklahoma City, OK; Aurora, CO
19 Years: Hialeah, FL (qualified voter requirement + 1 year of residence)
No Age Minimum Listed or Implied: Baton Rouge, LA; Minneapolis, MN; Pittsburgh, PA; Saint Paul, MN; Wichita, KS; Jersey City, NJ; Buffalo, NY; Yonkers, NY
Data unavailable: Birmingham, AL; Newark, NJ
Baltimore
City Comptroller, and City Council President: 25[3]
City Council Member: 21[3]