Pomona, Williams, Amherst, which has the strongest STEM program. Planning to study Bioengineering in grad school.
First, STEM is a broad and nebulous acronym, Science, Technology, Engineering and Math. You need to define if you want to approach it from the science angle, typically biology subfields, or engineering.
If you want the biology, any of them would be fine. They are all solid LACs, the differences of which would come down to intangibles.
If you want the engineering angle, I’d eliminate all of them and get an engineering degree.
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For graduate study in bioengineering, you may want to check the preferences that graduate programs have for undergraduate preparation. Examples:
https://www.brown.edu/academics/biomedical-engineering/academics/graduate-program/master-science-scm-programs/admission-requirements
https://be.ucsd.edu/grad/prospective-students/admissions/requirements
In some cases, an engineering undergraduate degree is preferred, but that is not available at the three colleges you mention. But there can be alternative lists of undergraduate course work that may be accepted, depending on the graduate program. Many of the needed courses (math through multivariable calculus, linear algebra, and differential equations; calculus-based physics; general and organic chemistry; general biology and biochemistry) should be widely available at colleges, but upper level courses and engineering courses may vary considerably in availability.
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We have this discussion a lot. If you have or are willing to spend the money for an extra year at Dartmouth, you can probably pursue bioengineering almost anywhere:
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To put that in perspective though, that’s a $420,000 degree if the applicant is full pay. You could pursue a graduate degree almost anywhere with a BME degree from almost anywhere with the right GPA and research experience.
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…anywhere but a good small college.
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I love all three of those schools. None of them offer engineering of any kind though.
So, you’re suggesting the OP forget about becoming a bioengineer?
If you’re interested in bioengineering, then I’d recommend one of these 153 schools that’s ABET-accredited in that area.
As you seem to have a preference for small to mid-sized schools with prestigious names (this thread, a previous thread with MIT, Harvard, Yale), then I would take a closer look at:
- Brown
- Bucknell
- Case Western
- Columbia
- Duke
- Fairfield
- Johns Hopkins
- Lehigh
- Northwestern
- U. Penn
- Rice
- U. of Rochester
- Tufts
- Tulane
- Union
- Vanderbilt
Are you a current senior? If so, where have you applied? What is your budget?
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It’s probably important to read all of the responses before replying 
@AustenNut - as per usual - has given an excellent alternative list of quality schools that in some ways mimic the OP’s preferences. Their replies are always welcome 
. But interestingly, it doesn’t include Dartmouth, arguably the premier “smallish to middle-sized” university in the country - and which has an engineering school.
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Pomona is one of the Claremont colleges. Harvey Mudd is the Claremont college with an Engineering program.
Williams has a specific Pre-Engineering Advising Program. Since your goal is to study Bioengineering in grad school, you might want to have a conversation directly with Professor Kate Jensen (kej2@williams.edu), the Pre-Engineering Advisor at Williams. She is in the best position to discuss the pros and cons of a Williams education as preparation for graduate study in biomedical engineering. They are very Frank on their website about the fact that Williams is not the place to study for anyone who wants to enter the jib market as an engineer directly from 4 years of college. So, I expect that they’d be frank with you about how Williams would fit with your aspirations. On the other hand, they do seem to have had success at preparing students for grad school in engineering.
Best of luck.
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Thank you for your kind comments. Dartmouth wasn’t included, however, as it wasn’t ABET accredited for biomedical engineering. As I am not an engineer, there may be other engineering fields that would work, but that I leave to the experts. 
I’m not an engineer either, but I wonder whether majoring in a specialty, as opposed to sampling it as part of a survey course, is really necessary, if your goal is to pursue it in graduate school anyway?
Entering a graduate engineering program without an engineering degree is challenging at some programs and impossible at many. Physics is the most common path for this option. Most other degrees don’t have the proper calculus and physics series, let alone statics, dynamics, thermodynamics, etc.
To add one to the list above fron @AustenNut - Lafayette College is a LAC that offers engineering.
That much is clear. I was wondering specifically about an A.B. or B.A. (as opposed to a B.S.) in engineering?
Why is Dartmouth the “premier” smallish to middle-sized university in the country?
It is a school where “fit” factors are strong, such as the heavy fraternity / sorority presence, D-plan, need for 1-3 extra quarters for an ABET-accredited engineering degree, etc…
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I’m old enough to remember when Dartmouth was on the cutting edge of computer science teaching and research in the country; its faculty and students developed BASIC which was the first computer language many people in my generation learned. I don’t think it can claim that mantle now but, in many ways it’s by choice. They’ve always believed themselves to be primarily a liberal arts institution. And it’s been resolute in the belief that you can’t - or shouldn’t - try to short shrift the liberal arts in order to pursue engineering. For that reason, the Thayer School of Engineering does not have an undergraduate counterpart. Dartmouth undergraduates who are interested in engineering have to invest in an extra 1-3 semesters of coursework in order to get a Dartmouth degree in engineering, the same degree they have made available to a handful of classic, premier LACs including:
Amherst
Bates
Bowdoin
Colby
Hamilton
Middlebury
Pomona
Wesleyan,
and Williams
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On the other hand, a student can earn an ABET-accredited engineering bachelor’s degree in four academic years while also taking substantial (required) liberal arts courses at other schools like MIT and Harvey Mudd.
| STEM GE | H/A/SS/W GE | FL | |
|---|---|---|---|
| Dartmouth | 4 courses (15 sh) | 8 courses (28 sh) | 1-3 courses (3.5-10.5 sh) |
| MIT | 9 courses (36 sh) | 8 courses (32 sh) | none |
| Harvey Mudd | 9* courses (32.5 sh) | 12 courses (35 sh) | none |
(sh = semester hours equivalent credit)
(* not including 1-1.5 sh labs attached to biology, chemistry, physics courses)
Note that both MIT and Harvey Mudd require concentrations within their H/A/SS general education, and such concentrations require courses more advanced than introductory level courses.