Bama, Arizona, Mississippi State, Ole Miss, Florida State, WVU and there’s likely more potentially, UAH for smaller. There may be others - Kansas, etc. U of SC will be borderline.
Some schools won’t offer Neuro per se but it’ll be in other majors.
Not sure what some prestige means.
Schools will have strong academics if the student pursues it.
Prestige is in the eye of the beholder. Besides, a neuro major will likely continue schooling.
A solid Honors college at a large public will be good.
You may look at some SUNYs too - they’d be “possible” to hit budget.
But at Arizona, for example, a 4.0 is $32K off of $40K - so you’re mid 20s and the Honors dorm is unreal.
Bama - you get $24K off $32K but one more ACT point or earning their special scholarship goes up to $28K - so $4k less - so also low-mid 20s.
The others have scholarship estimators and I’m sure there’s more. U Maine another.
PS - flying, driving - sometimes flying is easier.
When you have a tight budget - you have to have tradeoffs.
That said, what’s wrong with UNCW - as an example? Fine school. or App State.
CNU would be another to look at - should get close and is close.