To add some to what watsonwil posted for Houston:
A nice day trip, for someone of my mindset, might be to head out early and either go to NASA (Johnson) or alternatively, go to the Memorial at the San Jacinto Battlefield. That’ll bring you up to speed on Texas’ War of Independance quickly enough, and you can go to the top of the monument for a great view of the city. That all won’t take too long, and you can round out the morning across the road touring BB-35, the Battleship Texas.
From there it’s a quick zip down 146 to either stop and peruse the Boardwalk in Kemah, or continue on down to Galveston, where you can catch a few rays on the beaches, take a (free) ferry ride to the Bolivar Penninsula, visit Seawolf Park, or the Moody Gardens or, as I’m prone to, go next door and visit the Lone Star Flight Museum. For a completely privately funded effort, it’s pretty impressive. They have ~40 planes, mostly WWII era, and one thing you’ll notice is that most of them have oil drip pans below their engines. They fly these things!
They had an airshow down there a week ago and I believe the annual air show at Ellington Field (formerly Ellington AFB) was this weekend. Which brings to mind that we have various festivals throughout the year (Westheimer Arts Festival, Dickens on the Strand, Mardi Gras, Houston International Festival, etc.) that can be fun if you’re here when they’re happening.
And you can soon spend an afternoon at the Schlitterbahn Water Park.
If you’re like me, the LSFM can absorb some time, but the casual visitor could wrap it up with time to head back towards downtown via Highway 6 and get over to Brazos Bend State Park for a quick visit with the ‘gators. You’ll see a bunch and afternoon, when they’re snoozin’ in the sun, is the best time to visit because there’s nothing between you and them. If you want to stay until it’s dark, there’s also an observatory there.
Then back into town with time to change and head downtown for the evening. Go a little early, so you have time to look around. A staple of my tours for out of town visitors is a look at some of the incredible architecture in downtown Houston.
Then it’s off to the Theater District for dinner at any one of many great restaurants, finishing up in time to perhaps see a play at Jones Hall or see the Houston Grand Opera or the Houston Symphony. They all tend towards great. The one I attend most often is the Symphony, and that lets out at 10:00. A great time to amble on over to the State Bar of Texas, in the old Rice Hotel, or any of the other great bars within walking distance. If you’d rather ride, hire a horse carriage. It’s really amazing what a transformation has taken place in downtown Houston in the last decade. If you’re there during the day, the Downtown Aquarium is worth a visit.
watsonwil listed quite a few of Houston’s assets, and I must say that a “pretty decent Musuem District” is a modest description. I live on the border of the Museum District and the Montrose and visit the museums probably more than most. There’s no way one could do the Museum of Fine Arts Houston justice in two full days. The Menil, which sits about 50 yards from me right now, has one of the most extensive surrealist collections in existence. It’s a bit of a trip to see some surrealist Man Ray, Salvador Dali or whatever icon that you’ve seen reproduced elsewhere right in front of you, in the original. The Contemporary Arts Museum and the Museum of Natural Science bear mention as well. There’re 18 or 19 museums overall in the district.
While there’s nothing touristy to do there that I know of, if you’re in the Museum District/Hermann Park area, you can contemplate from there the Emerald City that is the Houston Medical Center. From the outside it appears as its own metropolis - I believe it’s the largest medical facility in the world.
While I’ve never done it (hmmm…, idea here?), you can book a waterborne tour of the Port of Houston, which is the second largest port in the country and the first in international shipping. Cool to see the big boats.
Other minor attractions might include The Orange Show and the Art Car Museum (which seems to stay rather small as the collection seems to move around - well, you know how cars are).
There’s more, but that’s it. I’m spent.