I wouldn't say it has great museums, having moved from Chicago to Houston as a kid. I found most of the museums... not as good in comparison. But Chicago has particularly good museums, so this might be unfair.
It does, however, have very good art museums specifically. And even more specifically, it has good art museums that are well-endowed enough to be cheap to visit. The Museum of Fine Arts Houston has one of the lowest entry fees of major metropolitan art museums, and the Menil Collection is completely free. Definitely a high-culture perk of the city.
Also, if you are willing to drive ~20-50 miles to visit something (and you had better be, if you are in Houston) there is NASA's Johnson Space Center, where you can see lots of rockets and rocket facilities; and Brazos Bend, where you can see lots of alligators.
I wasn't impressed with Chicago's Field Museum compared to HMNS, but I've only been there once, and IIRC there was renovation going on, so maybe I missed the good stuff. I'll give it another try next time I go to Chicago. Glad to hear someone is enjoying the MFA and Menil. The Menil was mostly the result of the Schlumbergers IIRC.
I lived in Clear Lake when I was young, and I was fortunate enough to get to hang out at JSC, and get really good access to the place. My Little League coach was an Astronaut. I can barely stand to go there anymore. It kills me.
Alligators? Yeah, and mosquitoes. I've seen enough of both.
On the science museum, part of my view, I think, is that HMNS is trying to do what two different Chicago museums are covering: the Field Museum (classic archaeology / natural science) and the Museum of Science and Industry (modern science, and technology of the industrial revolution to present).
The Chicago Field Museum is a classic "natural science" museum: a very large, multistory lobby greets you, with a monumental dinosaur reconstruction. The building is also impressive, from some century-ago world's fair. The rest of the exhibits, on the other hand, range from good to being quite obviously 100 years old with no love given in the preceding century (sometimes this is nice and quaint, sometimes annoying). It feels more impressive to me than HMNS, but HMNS might have better exhibits. The latter certainly has a nice gem collection.
But if you want something more sciencey, the Museum of Science and Industry is really nice. There's an entire simulation of a coal mine you can go down into, exhibits on the history of trains, on urban history, and on the history of agriculture, and even a captured German U-505 submarine. It was definitely my favorite museum as a kid, and I didn't find much like it in Houston.
It does, however, have very good art museums specifically. And even more specifically, it has good art museums that are well-endowed enough to be cheap to visit. The Museum of Fine Arts Houston has one of the lowest entry fees of major metropolitan art museums, and the Menil Collection is completely free. Definitely a high-culture perk of the city.
Also, if you are willing to drive ~20-50 miles to visit something (and you had better be, if you are in Houston) there is NASA's Johnson Space Center, where you can see lots of rockets and rocket facilities; and Brazos Bend, where you can see lots of alligators.