I would suggest Conn College and Haverford (since you’re looking at Bryn Mawr). I don’t believe that either has merit aid, however.
Why a double major? Does she really need to major in music, or does she just need to play in a quality orchestra and/or potential chamber groups and take private lessons? What would a music major offer her that performance opportunities and lessons won’t? If she wants to major in music, are we talking performance (BM)? Or maybe something more like music ethnicology? Is she entertaining a career in music, or is it just something she loves and wants to keep in her life (still continuing to learn with lessons, though)?
Once she has that sorted, she can start to decide whether to go the double degree route with a conservatory (Oberlin, Johns Hopkins, Bard, URochester/Eastman, Lawrence, etc.) or go the route with a college with a quality science program that has a solid orchestra. If the former, head over to the music major forums and start asking around.
For the latter, start checking out college websites to read about their music performance opportunities for non-majors and watching their orchestras on Youtube.
Here are some on your list that all have good science programs (these are just the ones I can speak to):
Oberlin: as a cellist who is not in the Con, she’ll likely have to play in the non-con orchestra. May or may not be up to her standards. Good merit possibilities. Eastman/U Rochester as a non-music major is the same.
Lawrence: little college with a solid physics program in particular. Non-majors have a very good chance of being included in the excellent con orchestra, more so than at any other conservatory. Very good merit possibilities. Check out their fly-in program for physics held every February if that is your D’s interest. Their high acceptance rate makes this a nice “likely” school for your list.
Bryn Mawr: joint orchestra with Haverford (rehearsals and performances are mostly at Haverford, too). Good merit possibilities.
Wellesley: joint orchestra with Brandeis (alternating each week between the two campuses). No merit. Lessons are free if you get any financial aid.
Claremont colleges: Not as familiar with these, but I believe they have a joint orchestra. Merit is most likely with Scripps, very competitive merit for Harvey Mudd).
Vassar: solid orchestra. No merit.
Smith: solid orchestra. Free lessons for those majoring or minoring in music, and some lesson scholarships even if you aren’t. Good merit possibilities. My daughter is very happy she is a science major playing music and taking instrument lessons here. 
It sounds like your daughter is coming from a strong HS music program. My D did as well and played in an excellent regional youth orchestra. She was disappointed to hear her friends a year or two older who went to some excellent colleges coming home over their breaks reporting that their college orchestras weren’t quite as good as the regional high school youth orchestra. So she made a point of contacting conductors at the colleges she was interested in to make appointments to play for them. Some of them had her join rehearsals so she got a sense of what the orchestras were really like. Also, some of the conductors said they could help her get accepted. I can’t help but think that her playing also increased her chances for merit aid (although there is no way to know for sure).
Two other schools: Skidmore and U of Richmond have some scholarships for instrumentalists (not necessarily music majors) who will play in the ensembles. They are both competitive. Skidmore’s is $15,000/year while URichmond’s is full tuition. URichmond also has science scholarships, too.
Be sure to check out Smith! Their STRIDE merit scholarships ($20,000 and a few at $25,000/year) include 2 years of paid research, which is an excellent opportunity for a science major. The conductor Jonathan Hirsh is well liked by his students.
My daughter was a state ranked number one player on her “endangered” Instrument as a tenth grader. She was in n auditioned children’s chorus, a orwcollwge wond ensembe and orchestra, and took both oboe and piano lessons. She was also in her HS ensembles, and played pianos and bells with the jazz band.
When college time came, she want to continue taking Instrument lessons and play in a college orchestra but not as a music major. That was her number one criteria. She was an engineering major.
She did contacted the private teachers, orchestra directors and music department chairs at ALL the colleges she was interested in applying to. They were very helpful and honestly answered her questions.
At the end of it all…she went to Santa Clara. She said the orchestra was not as good as her orecollwge orchestra, but she loved it…and played all four years…and took private lessons all four years (as an aside, her first private teacher was a CC poster).
For my kid…her…music was something she enjoyed, and found relaxing. She found it to be a welcome change from her science and math courses.
my kid thought she might minor in music…but that turned out to be more courses than she could manage with her double major.
This one of my kids never wanted to major in music.
ETA… Santa Clara gave her Instrument private lessons at no additional cost as long as she played in the orchestra…a 45 minute lesson every week. In addition, she got a small performance award each term…about $750 a year.
@Veryapparent, Your daughter might look at Williams. Rigorous academics, excellent sciences and math plus very strong music department. Double majoring is common and there are many performance opportunities, even for non-majors. The Berkshire Symphony, which is comprised of Williams students, Williams faculty and professional musicians from the area, is highly regarded. There are also student symphony and several other ensembles.
No merit, though.
I am with @LBowie while Vanderbilt is a great school with a great music program, it does not seem to be a good fit socially for your daughter (from the description you gave, you obviously know her better so maybe this is not fully correct). I was admitted to Vanderbilt this year, and it was in my top two of schools to consider, but my personality seems to be quite different than your daughter. I am very outspoken and extraverted, and I wanted Greek Life. Not only is Greek Life a big part of the school’s social life, but many of the girls there are dubbed “Vandy Girls” a term to describe the preppy, snobby, spoiled stereotype. And while stereotypes are obviously not universal truths about the people they address and are often exaggerated, its just something to think about.
OK so I think the issue with small schools is that you really need to visit them and some, like W&L are hard to evaluate during the summer. D (introvert/history nerd/piano playing) went to W&L. I wouldn’t advise it if you are adamant about avoiding Greek life, but I will say that all parties, etc are open and you certainly have option to not join. There is a good bit of camaraderie in the music department and they have beautiful facilities for small school. D loved that several piano practice rooms had Steinways and loved playing just to decompress. Later she resumed lessons with one of the piano professors (best piano teacher she ever had). She didn’t become a minor due to some of the group participation requirements that were hard to fit in for piano. Definitely more groups to play with when playing cello. She did do recitals including a senior one. One of best friends was cellist but not music major. If you qualify, there is some great financial aid but competitive is no need involved. Great school but I think one you need to visit to see if there is a fit.
Thanks that is very good to hear. The only reason W & L made list was HS counselor thought she would be a candidate for scholarship and our geographic location helped along those lines. Maybe good idea to include and see what happens. Our WC location makes touring difficult (almost a full day of travel for anywhere mid west, east coast) and I totally agree that summer trips are not particularly useful when evaluating for a “fit”. But if accepted would be worthwhile to fly out and see during school year.
@momrath
Yes, you are right about Williams! A great choice for top notch academics and performance opportunity with the Berkshire Orchestra. I forgot that one.
The University of Richmond has excellent music programs, strong sciences, and good opportunities for big merit for high stats students. They have approx. 3000 undergrads and give out approx. 45 full ride/full tuition awards to freshman each year, across many interest areas including science, and music/arts (arts scholars must major or minor in an arts area). One of my Ds graduated from UR last year, had a full ride science scholarship, and double majored in biochem/CS. She was very well prepared for Phd programs, and was accepted earlier this year to UVA, Duke, and UNC Chapel Hill. At UR, she was able to start working in a lab doing research during her freshman year, as well as having paid science internships each summer. Another D received a full tuition scholarship to attend UR, also a science scholar and is currently having a great experience, too.
Although my Ds have not been involved with music at UR, many of their friends have been, and have reported very positive experiences. Greek life is a presence on campus, but it does not dominate. UR frats and sororities are not residential. Neither of my Ds was interested in Greek life, but have some friends who joined, and others who did not. There are plenty of non-greek activities to get involved in.
The campus is beautiful and we have really grown to love Richmond on our many visits. It has an artsy vibe, great restaurants, museums, historical sites, parks, and outdoor activities. UR’s campus is about 10 mins from downtown Richmond, and has decent airport access, as well an Amtrak stop about 4 miles from campus.
You may want to consider University of Puget Sound as a safety. She could dual major or minor, they offer non music scholarships to some and she should see some nice merit there. It would be in the same bucket as St. Olaf. While it does have Greek, it’s very small and controlled by the school so relatively tame/low presence.
Lovely music program without the competition of a true conservatory.