My son is a junior and will be a senior next year. We’re looking for schools that he likes at might want to apply to early decision, since his counselor seems to think it’ll be easier for him to get into a school early decision. We have a list of safeties already. He has a 3.9 GPA and a 1490 on the new SAT. I would like him to go to an Ivy league school, especially since I’ve paid for him to go to a good private school. Education is important to me and I want him to receive the best education possible and to be challenged by the work and learn something, not just coast through college. I also feel that he has a good chance of being admitted, given his scores and the fact that he is African-American. His high school has small class sizes, and he wants to go to a college with small class sizes. He also wants to go to a college in a small town. We looked at some of the smaller Ivy League schools like Dartmouth and Princeton. He thought that the class sizes were too large and that he wouldn’t have the amount of access to professors that he’d like to have. We went to visit Bowdoin and Middlebury and liked those schools a lot more because they have smaller class sizes. I’m wondering what the reputation of these schools is. Are they comparable to the Ivy League? Do graduate schools hold these schools in a similar regard to Ivy League schools?
"Are they comparable to the Ivy League? "
I think that they are. Brunswick is also a lovely small town. I hope that you tried Gelato Fiasco while there (or if not, try it next time you visit Bowdoin).
They are all stellar. I’d argue that the small liberal arts school structure allows for a better undergraduate education and experience than the Ivies.
Does he have any thoughts on what he might like to study? There are other great LACs he could consider as well.
Graduate schools will hold them in equal regard to the Ivies. Look up Yale and Harvard’s current law school classes by undergraduate colleges represented. You will see these small liberal art colleges excelling. Look up the ‘undergraduate origins of PhDs’ that Reed likes to cite; you will see small liberal arts colleges doing better at producing future PhD’s than almost all the Ivies!
Random people? They will know Princeton and Harvard and Yale but they won’t know Middlebury and Bowdoin. Of course, they also may not know Brown or Dartmouth and will confuse U Penn with Penn State.
Williams grad here. Employers, graduate schools, and people who went to top schools of any sort say, “Wow! Williams.” Distant relatives, gas station attendants, check out counter folks, and other people you may encounter in daily life, for the most part, will ask, “Williams? Do you mean William and Mary? Roger Williams? Where is Williams?”
So, if you want bragging rights with the general populace, famous universities like Harvard and top sports colleges will give you more mileage than our nation’s top small liberal arts colleges. But if your concern is your child’s getting a job or getting into a graduate school, the top small liberal arts colleges will be held in equal regard to the top universities.
The people who matter - grad schools, employers of note, etc. - will know them. 
I would like to note that it’s been almost a month since a mob assaulted a professor and core academic values at Middlebury. Still, apparently, no one has been held to account.
If you care about intellectual diversity and respectfully engaging with diverse viewpoints, proceed with caution.
^You can’t assume due process isn’t taking place and decisions made about new rules without publicity though.
All in all, these schools are considered equal to Ivies by employers and graduate schools.
They’re not called, “little ivies” for nothing: https://en.wikipedia.org/wiki/Little_Ivies
If you are going to not go somewhere because of of a few imbeciles, then you will find yourself with very few choices of anything. You can’t let that stop you.
We’re all here on College Confidential, for example. 
By alumni achievements, they are Ivy-equivalents: http://talk.collegeconfidential.com/college-search-selection/1893105-ivy-equivalents-ranking-based-on-alumni-outcomes-take-2-1-p1.html
Short answer: Yes.
Short answer: Yes.
In my opinion, the quality of undergraduate education at A/B/M is if anything better than what you’re likely to get at most Ivies. Not only are you more likely to get consistently small classes at a LAC, but virtually all of those classes will be taught by professors (never by graduate teaching assistants). The downside is that LACs will have more limited selections of courses (and possibly of majors). Again IMO, the small classes and lack of TAs trump the narrower course selection (for most liberal arts majors, anyway).
By the way, as for the speaker referenced in post #5, his own daughter graduated from Middlebury.
In terms of admission to highly regarded law and business graduate schools, for example, Amherst and Middlebury are among the few schools that appear in both of these analyses:
https://www.■■■■■■■■■■■■■■■■■■■■■■/infographics/top-feeders-mba-programs
Here’s a snapshot answer with regard to graduate schools. Amherst graduates less than 450 students a year, and perhaps a few dozen go to law school each year. Yale Law School is the best law school in the country. Amherst currently has 18 of its graduates at Yale Law School.
To put that in perspective, that numbber is as much or more than several Ivies (even though the Ivies all are several times larger). On a per capita basis, Amherst currently has more people at Yale Law than any school in the nation other than Yale and Harvard. Heck, Amherst has more people at Yale Law than the entire Southeastern Conference, which has over 400,000 enrolled students.
Likewise, Middlebury and Bowdoin do very well with graduate school admissions - perhaps not quite as well as Amherst and Williams, but very well indeed. Graduate school admissions are a huge strength for the top LACs, even compared to the Ivies.