Hello! I am a female who has been accepted to these three schools. I am looking to either major in biomechanical engineering or mechanical engineering (I hope to somehow work in the medical field). I really want a school with a good social life (nothing crazy, but I do like to go out) and opportunities for internships and work-study. Also, location is somewhat important to me. I want to be in a friendly/collaborative environment where there are things to go out and do. Thank you so much for any opinions/advice 
I think there are older threads that compare these three schools. My bias is towards Case, being a Case parent.
For medical related work either CWRU or Rochester may be best. because of the associated Medical Schools in the same cities. At CWRU, there are two related medical schools (University Hospitals and Cleveland Clinic) walking distance from the undergraduate campus and solid mechanical and biomedical engineering programs.
This CWRU website talks about the new Health Education campus, that brings social workers, doctors, engineers, and nurses together to serve patients:
CWRU has an entrepreneurial program called Think Box, that helps business students and engineering students work together on new ventures: http://thinkbox.case.edu/
CWRU offers co ops in mechanical and biomedical engineering. These work assignments can be limited to summers so you graduate on time. Other students choose away semesters, making good salaries and no tuition is payed on the away semesters, allowing students to pay for much of their senior year.
https://engineering.case.edu/coop/
Cleveland is more urban than Troy NY, or Rochester, and offers both trains to get to the airport and West Side Market, and the Euclid Ave Bus to get to downtown quickly.
Cleveland neighborhoods are unique: Little Italy, Cleveland Heights, East Cleveland,Coventry, and various venues and clubs downtown. Right in the University Circle area,there are museums, Cleveland Orchestra, and LIttle Italy.
Sororities, and fraternities are popular at RPI and CWRU.
At CWRU , some Greek houses are very social, and some are more service oriented.
CWRU is a combination of a liberal arts college (Western Reserve College ) and a technical school (Case Institute of Tech) so the breadth of the education may be a little better than the more technically oriented RPI.
RPI students tend to be from New Jersey, New York, MA, PA. International students are less than 10%.
CWRU students are a little more heavily Ohio, Michigan, Indiana, Wisconsin, and Texas, with a good 20% from the northeast, and a balance from other states. 14% International students in the latest CWRU class.
Cleveland Institute of Music is right on campus and those students, take their general education at CWRU.
There are some joint CIM/Case music ensembles, like University Circle Wind Ensemble. Do not need to be a music major or minor to participate.There is some credit given.
CWRU has more women, overall, than RPI, but maybe not in mechanical engineering major.
Society of Women Engineers is active at CWRU.
RPI offers ICE HOCKEY to watch. RPI is more techy overall, so there will be a larger percentage of the campus
who also studies engineering and science. RPI offers a wonderful architecture program, CWRU does not offer architecture.
Both RPI and CWRU offer good business programs should you change your mind.
CWRU offers more foreign language classes and more humanities and social science classes, and some students who later will pursue law. RPI student body is somewhat more narrow, but quite a few students study business math and business there too.
Rochester seems to be a less interesting city to me. Troy is not really a city, more of an industrial town. Its not clear to me if RPI students go into Albany and its not really quite the same as Cleveland for theatre, music, clubs and fine art.
Also one cannot beat the thrill of the Cleveland Cavalier’s lately or the Cubs/Indians rivalry in Baseball.
Cleveland is a city in love with its sports teams, and Case students are enthusiastic.
My D’s an engineering student at RPI. I can’t comment on CWRU or Rochester since she didn’t apply to either of those so I’m not very familiar with them.
- Location: Troy is a small town, has been much improved in recent years and has a nice downtown area within walking distance of RPI campus. But it's not a big city, and neither is Albany really. NYC & Boston are both 2-3 hours away - more for weekend trips. My D has gone to each once in her 1.5 years at RPI so far. But if you like outdoors, RPI probably has the best setting of the three, with the Adirondacks national forest not far away.
- Social scene: RPI skews towards a nerdy student body (my D included). But there's the whole range of students, and plenty of frats and sororities, parties, etc. Lots of student clubs and things to do. On the other hand, having time to do those extras as an engineering student is another matter. Freshman year my D had time for clubs, but dropped them her sophomore year. But at least you'll be happy you're not an architecture major (they sleep under tables in the library and take coffee through IV drips :))
- Academics: The academics are very rigorous. My D said that she knows a number of students who have transfered in/out of RPI and they all say that RPI was tougher than where they went/came from. The upside is that lots of RPI grads are happy to see how much they know when they finish school, and employers know this too.
- Sports: Hockey is king. There are other sports (swimming, football, etc.) but they're not big.
- Other programs: As @Coloradomama said, RPI has a good business school that's very tech oriented. They're also one of the few universities with its own cognitive science department, and has one of the best game design programs in the country (and are very strong in CS in general), and an arts department with a focus on experimental/electronic arts.
- Internships/Co-ops: RPI has an excellent industry reputation, and getting internships/co-ops is very actively encouraged. The campus career fairs are attended by all the top companies, and while you still have to do your part, there are plenty of opportunities. Job placement after graduation (for engineering students) is very high as are average salaries.
- Student body: This is my D's favorite feature of the school. She's found the students to generally be quite diverse, tolerant, collaborative, helpful and friendly. She's made plenty of friends, and the lopsided guy/girl ratio hasn't been an issue.
- Medical: RPI is associated with the Albany Medical College and the hospital there, and offers an accelerate physician-scientist program with them, but I don't know much about it. (My D is ChemE, not BME)
If your long term goal is in the medical field, you would be best suited at CWRU or UofR as they both have affiliated local hospitals and all the internships and recruiters on their campuses that go along with it.
UofR / Strong is an integrated unit and is the largest employer in Rochester.
CWRU has the top two largest employers in Cleveland Clinic and University Hospital. CC is absolutely world class.
If you have never visited, I strongly suggest you to visit both.
Best of luck. Great choices, congrats.
Thanks everyone for your very helpful responses. I visited Rochester and loved it and I am visiting Case and RPI this week.
Have fun visiting them! I visited Case last week and really enjoyed it and will probably enroll there.
@insanedreamer Hi, I read your post and saw that your D is a ChemE student. As a prospective student looking into ChemE at RPI, would it be possible for you to tell me about her experience as a ChemE?