There are two Bush libraries in Texas. George H.W. Bush‘s library is at Texas A&M in College Station and George W. Bush‘s library is at SMU in Dallas. Both are worth a visit.
OP - lots of good options here.
I think the suggestion of visiting the national parks in far West Texas and southern New Mexico is a great one. They are all beautiful and very different from what you find in other areas.
If you prefer a more urban tour perhaps a stay in Arlington, which is in between Dallas and Fort Worth might be a nice option. Arlington has Six Flags, a couple of big water parks, and several of the sports stadiums. In the summer you are likely to be able to see a Rangers game. Their new stadium is very nice and as the Rangers haven’t had great seasons lately, the tickets are not very expensive.
Both Dallas and Fort Worth have excellent zoos, beautiful art museums, botanical gardens, and outstanding science centers. The Dallas world aquarium is also worth a trip. Fort Worth is more Western oriented and the stockyards are a lot of fun. In Dallas visit to the Sixth Floor Museum, and Reunion tower are worthwhile.
Fort Worth is also home to one of the US bureaus of engraving and printing where you can see how they make the money.