I would look at your list of schools and drill-down into the majors and course work. Some might not have the major you want or you might not like how the classes are structured. For engineering are the schools ABET accredited?
Also, travel costs can add-up. I would have a few more on your list. I’m assuming UT-Austin or UT-Dallas? Some people will disagree but college apps take time. There’s always more essays to write. Personally, I think any more than 10-12 gets hard to manage. Quality over quantity.
Of the schools on your list Yale might check all the boxes. At least all the posts on CC point to how much help Yale provides for its students.