My sister lives in the Jersey Village part of Houston, which is essentially right there. When I visited once, we ate at Los Cucos, which was fantastic:
290 @ La Taquiza
It is a local Houston chain; they have about 10 or so locations around the area.
Are you actually flying out of HOU, or did you use that to designate Houston? If you are indeed flying out of HOU, the NASA visitors' center isn't terribly far, at least compared with IAH
Southwest flies in/out of HOU, as do a few other carriers, UA has a major hub at IAH, and most major carriers fly there, with the exception of Southwest.
As far as museums, I'd check the site for the Houston Museum District:
Houston Museum District
Most things in Texas have funky hours on Sundays, if they are open at all. I wouldn't be surprised if some things open as late as noon, but definitely check first.
If you want to do something interesting, the Port of Houston has free boat tours (I've done it once):
https://porthouston.com/sam-houston-boat-tour/
It isn't glamorous, but more educational.
As far as the NW area, it is perfectly fine. My sister loves that area, with the exception of floods (they were hit hard by Harvey). They like it enough that they, and most of their neighbors, have rebuilt to stay there.