Mostly hotel questions – downtown or farther out?

We’re traveling to TX in March to see family (San Antonio) and some exhibits (Houston). We’ll have a car. My questions are mostly about hotels and transportation. I’m assuming that we won’t want to drive to see museums in the museum district. Please let me know if I’m wrong about this.

Would it be better to stay downtown (pricey hotel + parking fees) or farther out along a bus route? I’ve read here about using the Metro(?) app – there seem to be several choices. Which one should I get?

I’m much more familiar with public transportation in the NYC area. Most of the park ‘n ride lots there require parking permits unless you’re far from the city. Is that also true in Houston?

Finally – does anyone know when tickets go on sale for NASA’s Johnson Space Center? So far there’s nothing available past the end of this month.

Thanks for your help. We’re looking forward to some time away from cold and snow.