having some of the biggest cities in the US means a plethora of museums. though they don't rank up there with my favorites in the US (the art institute of chicago, MOMA in nyc, the de young in SF, and the field museum, also in chicago), they are definitely nothing to complain about.
this is the modern art museum in ft. worth, which i have waxed poetic about in the past. we also have the amazing (and free!) kimbell museum here, the ft. worth museum of natural history, as well as the amon carter.
dallas has the DMA as well as a science museum i have never been too. austin has two remarkable and under the radar museums that are my favorite - laguna gloria and elisabet ney - as well as some more mainstream ones.
houston is full of them, though i have to admit i have spent very little time there.
add to this the many across the state in other locales and i think you will find we are more than well-equipped in this area.