That's a hard question to answer without info, because Texas is so big and has such a diverse landscape. I can give you better tips if I know what you're looking for, whether it be historical sight-seeing, nature & wildlife, outdoor sports, whatever you're into.
If you come through Northeast Texas I'd be happy to say hello, but there isn't much tourist stuff here. Mostly farms, lakes, and little towns with a couple of medium size cities.
If you went to, say, Austin, San Antonio would be close, so you'd have the Capitol in Austin, and they have a famous night life on 6th street with the clubs & all, and in San Antonio they have the Alamo and the River Walk. And New Braunfels is nearby, and they have awesome tubing on the Comal River.
The state has a website on tourism: https://www.traveltexas.com/#/
Be careful in our big cities. The diversity is real, lol!
Anyway, I hope the website helps and if you want to tell me what you're into, I'll try to give you some better information.
BTW, my stepmother is a native Swede, from Kalix.