$40-60K is a large delta, of course - hopefully you can narrow that down.
One thing your family can do is a Net Price Calculator. It will show if you’d get aid. For example, the Ivies may not be great for your major. Cornell would be - but it’s not the urban type environment you’d want. But Carnegie Mellon is. Have them fill out the NPC - would you get aid? Same with MIT.
Close to your budget would be UWash - but it has a 2% OOS acceptance rate.
Georgia Tech is in Atlanta - a red state but very blue and diverse city.
UMD is another that could work - but - it’s pushing the budget - if your budget really goes up to $60K. There’s a small chance of merit.
A school like UMN is strong - and would be a home run for you. And you’d easily get in I think. Pitt is another that’s strong - really - in many majors.
Those are top schools - but you might look at Arizona, U Oregon, and then you have some in states of course - a few UCs and maybe an SDSU.
If you find out money is an issue, I noted other schools above because - you likely have the NM golden ticket.
Tulsa is in the outskirts of a city - and assuming NMSF, you’d go for free. It doesn’t hit your midsize to large and it’s not liberal - but it is free - and if you find out that matters to your family. UTD is on the outskirts of Dallas - which has liberal parts - is extremely diverse and has a great NMF plan. It’s a safety for you.
And there’s more.
But you’ll certainly have many great options. You’d need to make sure that your list is diverse enough.
You could look at a Brown or Columbia for example - but again, have your parents run the Net Price Calculator - because if your budget is $60K and they’re $90K+, that doesn’t work, etc.
Many schools mentioned are high reaches but at the same time, you could, in theory, get into any school.
Best of luck.