Look at Union College–it offers good merit and has a wide selection of engineering options in an LAC setting
Olin–just look at it. Truly unique but all engineering
Swarthmore has engineering and good FA
Haverford has a 4+1 engineering program with UPenn, that includes a masters degree. It’s part of the same consortium as Bryn Mawr, Swarthmore and UPenn–all excellent schools. If you identify as female, Bryn Mawr has the same 4+1 program.
If you have the scores, look at the Claremont Consortium-- includes Pamona, Harvey Mudd, Scripps, and Pitzer and Claremont-M.
As others have noted, NM Tech is cheap and excellent. Also Alabama has merit for OOS. And consider also South Dakota Mines and Tech–cheap OOS tuition relatively speaking
University of Maine Orono is matching flagship tuition in all other states, and it has an engineering program. Also Maine is gorgeous. So there’s that.
If you identify as female, look at Smith’s engineering program. Smith is part of a consortium with UMass Amherst, And Wellesley has cross registration with MIT.
If you have high scores, also consider Clarkson U. They may give you merit.
These may be too specialized, but SUNY Nanotechnology is a teensie program that may want to attract you if you have great scores. I believe it’s the only undergrad nanotech program in the country.
Similarly, there’s a really cool engineering program at Alfred – glass engineering. The program was started with funding (I believe) from Corning–groundbreaking company in terms of glass technologies over the years. It’s worth just going to the website to look at what they offer. Again: super cool IMHO. And if you have the scores, you might get merit there. I believe that it’s the only undergraduate program of glass engineering in the country,maybe this hemisphere, Not entirely sure but I think it’s fairly unique. https://engineering.alfred.edu/undergrad/ges/