Scores of American cities from Hartford, Conn., to San Francisco elect mayors today in a generally low-key, off-year election that also features numerous ballot amendments ranging from betting proposals for Texas to a third vote in Maine on whether to shut down a nuclear power plant.

In the major mayoral races:

Philadelphia: W. Wilson Goode (D), the city's first black mayor, is slightly favored over the flamboyant Frank Rizzo, the Democrat-turned-Republican who was mayor from 1972-1980.

Miami: Xavier Suarez, the first Cuban-born mayor in the nation, faces four challengers, but is the favorite.

San Francisco: With Mayor Dianne Feinstein (D) unable to run again, Assemblyman Art Agnos had a slight edge over John Molinari, a 16-year member of the Board of Supervisors, and 10 others.

Hartford, Conn.: Democrat Carrie Saxon-Perry is heavily favored to defeat Republican Philip Steele to become New England's first black woman mayor.

Tucson: Republican William Gilkinson, the city's former police chief, is in a close race with Democrat Thomas Volgy, who has been on the City Council for 10 years.

Charleston, S.C.: Mayor Joseph P. Riley Jr. is strongly favored for a fourth term over Republican Roy DeHaven.

The New Jersey Legislature is up for grabs. It now is divided, with Democrats holding the Senate and Republicans the Assembly. Without popular Republican Gov. Thomas H. Kean at the top of the ticket, Democrats think they have a chance to win the Assembly.

Among the major ballot issues are: legalizing parimutuel wagering on horse racing statewide in Texas and dog races in coastal counties; Maine's third vote on closing the Maine Yankee Nuclear plant; and whether to build a downtown baseball stadium in San Francisco to replace Candlestick Park.