There’s many more - small, medium, large - it just depends on not what you can spend but what you want to spend, where you’re from, where you want to end up.
I do agree that you have to figure out what you will get aid wise. Every situation is different of course. But I think given your income and likely assets, aid is unlikely.
But hopefully I’m wrong.
The important thing to know is - that likely every state flagship has tons of brilliant kids. That’s why there’s more NMFs at public schools (ones you’d never think of with the most being at Bama) - which btw - you’d be out at Bama for under $200K for both kids combined and they have the Blount Scholars, Randall Research Scholars - in addition to the Honors college. That’s just one example of many - that would keep a few hundy more thousand in your bank!!
Hope you keep us posted on your journey.