Hallo! Wie gehts?
Dallas and Houston are both financial sectors of the state. Dallas isn't necessarily the city you'd want to visit if you're looking for Texan culture, as it is often classified as a Midwestern American city. It lacks that charm the more southern cities have. It of course has amazing restaurants, museums, parks, etc but it's definitely not something I'd go out of my way to experience (especially coming from Europe). The Dallas/Fort Worth metroplex (a term used in the States to mean an area containing many big cities) is just huge, congested, and stressful. It's a nice place to live, but I wouldn't want to visit as a visitor.
Houston is more of a Texan city in terms of culture, but it is also a very big business city. It's sometimes called the New York of the South because you can drive a few kilometers and see Vietnamese, Chinese, Eastern European (and some Western), American, and Middle Eastern cultures just thrown into a big mixing pot. It's just not much different than the other big American cities, in my opinion. If you're looking for Texas, I'd go elsewhere!
San Antonio is a huge city, by the way. One of the largest in the state. It's definitely one of the more "Texan" cities. Lots of culture to be seen and some fantastic food. You must try some tacos made by little old fat Mexican ladies that speak only Spanish! I'd go see the sights downtown, which are really pretty. The riverwalk is a must. See the Alamo, for sure. Although it's a bit of a tourist trap in my opinion. Haha, and New Berlin is such a small village, you'd drive through it and not realize you were there.
And most definitely Austin! It's such a weird and charming city. Definitely as Texan as they come. Coming from Europe, I think you'll feel most comfortable there. Very liberal and socially progressive. The best live music in the country and some great food and sights as well.
Ja, meine Urgroßväter Familie aus Bayern. The english word for Urgroßvater is great-grandfather. Grandfather's father. Texas Germans are dying off, though. He spoke it around me when I was a little kid so I picked up some words. I've tried studying it, but German is so difficult! I just know a few words and phrases. The grammar is especially difficult. I've heard Bavarian is a bit different, what with the pronunciations of words! Spanish is a much more common language here, so I've been learning that.
I think you'll enjoy your time here and find out most of those stereotypes we have aren't true. Just try some tacos and bbq and make friends with the locals. We absolutely love Europeans.