In the end, how much can you pay - whether from a 529 or from cash flow or investments or all of the above.
BC, as an example, is $72K just for tuition. $90K with room and board - so you need to ensure you have need or take it off.
You can find Jesuit schools - like Loyola Chicago, Maryland - I don’t know if they’ll hit your price but might. Seton Hall might get close.
You noted SE - you’d easily hit cost at large (and very Greek but still most aren’t) - U Alabama - with a 1450 ACT, you’d be $23K or so for tuition room and board.
A bit smaller and less crazy is Mississippi State and even smaller - 10K kids - is UAH. These are publics. There’s other smaller publics too - but when you are out of state, most charge more. But these have auto merit and can get you in the low 20s. There’s others too to get you under budget - Tennessee Chattanooga, as an example.
In the NE, U Maine will likely match Rutgers tuition. The SUNYs can be lower cost - you might try a New Paltz or Oswego.
You can find regionals that are smaller like TCNJ or Millersville in PA or Salisbury in Maryland to hit budget.
You can maybe squeeze into to an LAC like Kalamazoo.
If you qualify for need, you should fill out a net price calculator to see.
I put U of Rochester below - they meet need.
Let us know how that goes.
Research is (or was b4 funding cuts) fairly widely available if kids ask…internships are more based on the kid than the school. But if you’re in, for example Huntsville Alabama - UAH - you have defense companies galore. If you’re in Oswego NY - not so much but that doesn’t preclude you from finding an internship in the summer.