I strongly recommend the San Antonio complex of missaions sites operated by 
NPS (the Alamo is there, too, but intrepreted at a much poorer level).   
One could spend several days there and include the nice River Walk downtown.   
This is ca. 2 hours S of Austin via an interstate that has a great roadside 
sn ake museum.

Top the East is the Ships of Discovery exhibit at Corpus Christi, featuring 
early exporation of the Texas coast by Spaniards and French.

To the north is Washington of the Brazos, an early capital of Texas, 
located near Houston., and the German settlements near Fredickburg. Also a visit 
to the Museum of Homesteading is interesting.   You do not want to miss the 
SHA tour of the Institute of Nautical Archaeology at College Station.   This 
is the world center of underwater archaeology.

To the west is the site of San Saba Mission.

I can't help you much with the dude ranches, because every male here in 
southern California is called "dude", even those with Ph.D.s.   I am about to 
explore the area of Brownsville myself this January and maybe try slipping 
into Mexico if I feel lucky and highly insured.

Bob Hoover