Do I need to take the recommended course in order to gain more ad opportunity?

I have been staying in Houston for 3 years and I’ve never been to any other states in US.
If all the top public schools don’t accept me, I guess I will still have University of Houston.
But I do want to go to another state to experience life with more diversity.
I’m just afraid if it’s not a top school it will be hard for me to look for a job after graduate.