My kid finished up her 15 common app college applications. They include selective LACs, which are known for offering merit-based scholarships (we don’t qualify for any financial aid) that will bring our COA down to below $60K. Example schools include Scripps.
What are some other ones she can apply to? She has a ubiquitous degree (Chem) and just wants a nice, pretty campus.
Why do they need to be selective? Do you think anyone has heard of many of them?
You can get COA very low at great schools - and if you look at leading chem schools, your top for PHD (per Capita) are Juniata, Kalamazoo (you’re probably $40K there), Wabash, Allegheny (another likely $40K), Wooster.
Grinnell has merit - it’s top flight - but below these in PhD per Capita.
Hendrix is on the list - and it will match your in-state tuition. Fine school.
Rhodes likely comes in $40K.
Susquehanna less than that. Willamette and Furman are both great names. Furman is very nice.
You don’t need selective per se. You need to hit a price point.
Most LACs don’t have the “heft” to pull off full pay - so loads out there give great discounts.
Beauty is in the eye of the beholder but Rhodes and Sewanee are very nice. W&L to me is the nicest - but not gonna get merit now there.
But when you have a budget, that’s what needs to lead with.
Based on your daughter’s interest in chemistry, perhaps consider colleges with notable lab facilities. Lake Forest, for example, appears in this site:
Best Colleges for Science Lab Facilities | The Princeton Review
As another idea, look into Wheaton (MA), which also offers excellent science facilities.
Do you have any geographic preferences?
One daughter was offered merit aid at Bennington College which brought it well under $60k/year. Our other daughter was looking at small “primarily undergraduate” universities in Eastern Canada (the Canadian equivalent of a LAC). She applied to Acadia, Bishop’s, Mount Allison, and St. Francis Xavier. All would be under US$60k / year even for an international student without merit aid (note the exchange rate, although I think they might be under C$60,000 per year). Also merit aid is possible. Mount Allison is usually ranked as the top small primarily undergraduate university in Canada, although the other three are very good also.
All five of these schools are in attractive locations with attractive campuses.
I second asking if there is any geographic preference
Additionally, it might help to know where she has already applied so that you aren’t receiving suggestions on schools that she has already submitted to 
Student academic qualifications would help others help you, since likelihood of merit scholarships at schools that offer them depends on how the student’s academic qualifications compare to those of other admitted students.
A student reaching for the school is less likely to get merit (even if admitted) than a student for whom the school is likely for admission.
As another suggestion, consider St. Olaf.
I don’t know how many of these would get your COA down to $60,000 (many would), but LACs with good merit include Grinnell, Macalester, Conn College, St. Olaf, Beloit, Mount Holyoke, Oberlin, Bryn Mawr, and Sarah Lawrence. I don’t have personal experience with all of them, but my D23 had merit offers from many of these having applied RD (Mac, Conn, Mount Holyoke, Sarah Lawrence).
I’m finding it hard to formulate a response that doesn’t feel like a waste of my, and OPs time without knowing what schools the student has already applied to and what they consider selective. Scripps as anchor is not that helpful to me other than telling me they are open to women’s colleges, but maybe not if they are less selective than Scripps. If OP comes back with some more information on at least basic stats, where student has already applied, if there is a selectivity threshold they have in mind (e.g. 40% or less admissions rate), any geographic limitations, then I can think on it more seriously.
Other selective LACs I know give merit $: Gettysburg, Bucknell & Muhlenberg College in PA. Denison & Kenyon in Ohio, Union College & St. Lawrence in New York and Whitman in Washington. Good luck!
My S25 was offered merit that brought costs below $60K at the following LACs: Oberlin, Dickinson, St. Olaf, Connecticut College, Wheaton (MA), & Clark University (very LAC-like). Skidmore has a couple of STEM-focused scholarships also. His friend at Mt. Holyoke got significant merit as a STEM major.
Obviously this is just a starting point and not definitive, but you might want to check out the per capita version of this list of feeders to PhD programs, specifically the Chemistry list:
https://www.■■■■■■■■■■■■■■■■■■■■■■/dataverse/top-feeders-phd-programs#chemistry
You can then cross-reference that list with this merit aid list:
https://www.■■■■■■■■■■■■■■■■■■■■■■/dataverse/merit-aid
If do that, you will see colleges like Kalamazoo pop up favorably on both lists. I happen to know a little about Kalamazoo–it is an older LAC with a pretty classical campus, and a cool curriculum structure they call the K Plan. It shares a fun college town of the same name with Western Michigan, and in fact the town of Kalamazoo is well-located between Chicago and Detroit, and has become a bit of life and related sciences hub. Definitely seems worth checking out to me.
A non-exclusive list of others high on both lists I know enough about to recommend for consideration include Juniata, Allegheny, College of Wooster, Hendrix (note it actually starts a lot less expensive), St Olaf, and Earlham–and this was just scanning the Top 20 on the Chem list.
To which 16 schools has your daughter already applied?