Trip to Houston, what is public transit like?

I will be going to Houston in a few months for a cruise. We will be spending a few extra days in the city to do some touristy things. I would rather not rent a car or uber if I don't have to. What is the public transit system like?

We will be staying downtown, plan on going to premium outlets, the space centre, and the cruise terminal

Would that be possible on public transit or would we need a vehicle?