Places generally along the South Freeway (I-45), and south of the Ship Channel, including Clear Lake, Deer Park, Freindswood, the Hobby Area, League City, Pasadena, Santa Fe, South Houston, and Texas City.
At this point, I don't think that they'll approve them. At least with scooters in the form that they are in now. Lime just had a pretty significant service retraction.
They left San Antonio, Atlanta, Phoenix, and more: https://news.crunchbase.com/news/as-lime-leaves-12-markets-a-note-on-scooters/
Also, I'm pretty sure the new CoH Sustainability project thing went out of its way to not mention scooters. It said multi-modality transport, but then mentioned bike share and car sharing.
Bill Williams' restaurant was in the 6500 block of Main, which is indeed at Dryden at Main (where the Bioscience Research Collaborative building is located now). I've seen a Bill Williams menu from the 1940s that gives its location as "on South Main, across from Rice Stadium", but that would have been referring to the old Rice stadium, where the track is now, not the current one that was erected in 1950.