The Babe Didrikson Zaharias Museum is a small, round building in a park adjacent to I-10 that also serves as the Beaumont Visitors Center. Inside is a vast collection of memorabilia from her athletic career. The highlight, in my opinion, is her gold medals from the 1932 Los Angeles Olympics. This museum is so close to I-10, that even if one were merely passing through Beaumont, I would highly recommend a "leg-stretching stop" there to take a look. Honestly, it would add as little as ten minutes to your trip.
Just north of Beaumont is the Big Thicket National Preserve.
Click here for Big Thicket National Preserve Travelogue