What to do in surrounding areas of Katy or Sugarland as an introvert?

I(25f) may move to Houston soon for a job. I'm an introvert so it would be easy for me to just stay at home since I have no idea on how I should spend my free time outside of my house. And by me living on my own for a while.

Any safe places that seem cool for an introvert to visit? I hate the idea of partying and drinking. So any places associated with that is a no-go. I do enjoy traveling to very quiet diverse areas and as a black american who takes interest in being around all walks of life.

Anything involving Korean culture(restaurants, stores, etc.) would be nice too!