Colleges with Mechanical Engineering and Smaller School Feel

@Tara108 Cooper is a great choice especially w/ the high scores, they have great engineering and give
a 21K scholarship to all accepted students: https://cooper.edu/admissions/financial-aid
Bucknell & Lehigh ¶ are both great smaller schools w/ strong engineering. Rose-Hulman (Indiana) is like Olin but larger and somewhat less selective (still has very strong engineering). RPI (NY), WPI(MA) if your student is ok with little to no humanities present. Harvey Mudd (CA) is the top engineering/STEM LAC with access to the 7 College Claremont College Consortium in Claremont, CA. Dartmouth is an undergrad-focused Ivy with strong engineering.

CU says that 62% of their students are from the states of New York or New Jersey, including 37% from New York City specifically. I would bet that large numbers of these students are living at home and commuting. If your home was within commuting distance, CU could be a great value, given their good financial aid.
http://cooper.edu/admissions/facts

But if you are non-local and want to live near campus, then the value proposition changes. Check out the advertised rents for the campus area (note that many of these are 2-bedroom or 3-bedroom apartments, so a share of the rent would only be a corresponding fraction of the posted cost):
https://www.renthop.com/nyc/cooper-union-apartments-for-rent

Swarthmore?

Take a look at Alfred University in western NY.

Thanks to all! Very helpful indeed.

Don’t rule out Rice simply because of its Texas location. Houston is an incredibly diverse city, and its politics skew well to the left.

In some ways Rice is a kind of over-sized liberal arts college, and–as such–it combines traditional advantages of a LAC (e.g., focus on undergraduate instruction, collaborative atmosphere, etc.) with those of a research university.

LMU and USD in So Cal, Co School of Mines and Or Inst of Tech are both WUE participants and worth a look.

Oregon Tech is WUE, but not very selective.

Colorado School of Mines is a more selective and attractive option, but based on my reading of the FAQs on the CSM website, they may not, in fact, be WUE:

https://inside.mines.edu/Frequently-Asked-Questions-New-Students_1

But OP said he wasn’t looking for a Rocky Mtn location. Why? Who knows.

WUE participants are typically less selective ones. The more selective schools in those states are not likely to want to offer tuition discounts to WUE out-of-state students when they could easily fill their out-of-state seats with those paying list price. So, out of the “mines” schools, the ones in NM and SD are in WUE, but the one in CO is not.