The Amon Carter Museum is one of the nation's preeminent collections of American art in general, and specifically photography and "western" art. Admission to the permanent collection is always free, which is a bonus! (Call for ticket prices to special exhibitions.)

See the list of current exhibitions here: http://www.cartermuseum.org/exhibitions

Hours:
Tuesday, Wednesday, Friday, Saturday:
10 a.m.–5 p.m.
Thursday: 10 a.m.–8 p.m.
Sunday: Noon–5 p.m.
Closed Mondays and major holidays.

Find out more information here:
http://www.cartermuseum.org/