The winner is all archaeological site museums

And the runners up are....

Mexico City, D.F.

Mexico's best archaeology museum, an amazing museum at the ruins of Tenochtitlan, at the Zocalo, plus dozens of other museums

Guadalajara, Jalisco

Many museums of art, culture, and its fine ceramics tradition

Xalapa, Veracruz

The archaeological museum is one of the finest in the country.

Oaxaca, Oaxaca

Lovely cultural museum housed in monks' cells, at Santo Domingo monastery. Good museums of contemporary art (MACO), and archaeological finds at Museo Rufino Tamayo

Guanajuato, Guanajuato

Diego Rivera Museum, Quijote Museum, Mummy Museum, and others

Veracruz, Veracruz

Tour ruined San Juan de Ulua Fort; city museum & maritime museum

Zacatecas, Zacatecas

Several great museums including a mask museum .

Morelia, Michoacan

Fine art and several small regional history museums

Campeche, Campeche

Small museums in pirate-proof bastions of yore