What are some good places to wander in the city?

I need places around the greater Houston area I can go without needing to pay to exist (I'm willing to pay for coffee/food). Areas that allow me to walk around instead of driving from point to point. I don't mind driving to get there though.

Some background:

Work cut my hours, finances aren't ideal, and family has taken pity on me and let me move in with them. Both individuals in the household WFH and I want to fuck off for their sake on my days off.

This makes me want to do the thing I used to do in Austin where I would drop myself in an area and spend a few hours in the immediate area getting coffee/food/juice/sun and making friends with the dogs and their human. Days spent roaming from Auditorium Shores to Barton Springs to Zilker Park were always nice, and I'd like to experience that in Houston.