Case is a small private research university with 5000 or so students. Very well regarded. The students we know that attended all did super well. Has a bit of an artsy STEM vibe. Many people draw comparisons between Case and U of Rochester.
Case is in an area of Cleveland adjacent to a number of museums. It’s referred to as the “Oval.” The art museum, botanic garden, history museum, children’s museum, and the symphony’s Severence Hall are all right there. It’s an urban campus but plenty of green space. There is an outdoors club and a hiking club. NE Ohio is actually very beautiful and has great hiking an easy drive from campus.
Cleveland as a whole has had a beautiful resurgence since the recession. It’s a great small city! Would recommend adding it to the list to research.
For physics and LAC’s I am surprised nobody mentioned Lawrence U(WI) yet. Also, if you are looking for less selective small engineering schools, there are places like Milwaukee School of Engineering.
As you explore more LACs, you will note that in some cases the largest academic building on campus will be dedicated to a college’s science facilities.
If engineering is the primary interest, consider small engineering focused schools. SD, NM, CO, MO, and a few other states have public schools of this type. There are also various small private engineering focused schools like IIT, RHIT, MSOE, WPI, Caltech, Harvey Mudd, Stevens, Kettering, etc… Harvey Mudd is also considered a LAC.
3+2 programs seems to be well marketed, but consider the hurdles that often prevent transfer to the “2” school: cost of an extra year, not knowing FA at the “2” school, not getting admitted to the “2” school as a transfer. So if engineering is a strong interest, it is best to choose a college where it is available natively.
Physics has a fairly well defined set of core courses for the major. Check that they all exist and are offered frequently enough (statistical / thermal physics is often the one offered least frequently). Bigger physics departments may offer additional electives.
Math is a broad subject with many subareas. Take a look at the catalog of a college with a big math department, then compare the offerings of the smaller schools of interest to see what they cover.
Harvey Mudd. Literally only has STEM majors, though of course you do have to take humanities courses, which you can do either at Mudd or at any of the other 4 colleges in the consortium