im the dad, sorry but im from another country
I'll try to help you the best I can.
Assumptions:
Your daughter will be an international student, therefore, financial aid may or may not be available as a non-American, depending on the school. Which Ivies offer international students money, I am not sure, but very few US colleges give merit awards or finaid to international students.
If the quality of education and playing on the team is most important, as opposed to a possible future pro tennis career, than go Ivy, or look into some D III NESCAC colleges, such as Middlebury--finaid is offered to foreign students--where the academics are as good as the Ivies, but class sizes are even smaller, and the profs are there to teach and help students only. If the prof's office hours at 2pm-5pm, he/she will be there for your daughter, from 2pm-5pm, without fail. Even look into Seven Sisters, such as Welsley, Smith, or Holyoke. Your daughter will be a superstar on court there and have friends for life.
Firstly, the particular Ivy is very important. I assume that you do not want to mention which one(s) on the net. Therefore, I offer the following:
HYP:
Harvard's undergrad experience is less optimal than Yale or Princeton. There are many Harvard alum who prefer to send their kids to Yale instead.
Yale requires 4 more courses, 36 total, to graduate, so you will be stressed for four semesters where you take 5 courses. Remember, most Ivies, use the liberal arts system rather than the university system, and a liberal arts course requires much more in-depth examination tha a 3 credit university course. At Yale, you must stay in the immediate college town area. Outside of that area, is definitely not the best. The coach has been there for 2 years, and she is very young.
Princeton is ideal, and so is the town, which is not just a college town, but a fully supported upscale community. Of the three, it is the smallest. Class sizes are very small, and professors are very accessible. They just hired a new, and very young coach.
Dartmouth/Brown: True liberal arts Ivies. Dartmouth consistently ranks as the highest rated college for student satisfaction in the country. Town is similar to Princeton's. Brown is integrated into the small city of Providence, and very safe. You are also 45 min to Boston if looking for night life or parties at any of the Boston colleges, where there are many. Brown also lets you take any 32 courses of your choice. Both have small class sizes as well.
The Brown coach is new, has quite a record from where he came, and is nationally known as the author of "Pressure Tennis". The Dartmouth coach has been coaching his whole life since graduation, he is quirky, but well liked. With both coaches, you can trust your daughter to be taken care of if something happened, and you need a surrogate parent until your plane gets there.
Columbia: you are on the Upper Westside, and gentrification has taken over the northern area of the campus. It is very safe, and of course, you are in NYC. It is the ultimate sink-or-swim school. The profs are there to help, but anyone who comes to NYC is expected to be crazy independent. The coach is very young, and the assistant coach just got hired.
Cornell: the most beautiful of all of the Ivies. It is a true university, and very difficult to get "A's". Everything is graded on a Bell Curve, so if everyone gets a 95-99 on an exam, than all of the 95's receive an "F", and all of the 99's get an "A". Everything in-between is a "B/C/D". That's tough!. The coach just took over both men's and women's tennis, and came from a winning program in the *******. You can trust your daughter to be taken care of if something happened, and you need a surrogate parent until your plane gets there.
Penn: Like Columbia in many ways, but once you leave the four college campus area, you need a body guard. You must stay by the wharf, on South St., or historic areas. However, it is a very quaint and historic city. The student body is 35% Jewish, if that has any meaning to you for any reason. The coach is new and very young. They have had a lot of turnover for both men's and women's tennis. If she goes to Penn, go for the academics; you'll never know how long the coach will be there.
Ivies stress academics first. If there is a choice between class and tennis, you will go to class, and the coach will not only agree, but be supportive, as long as you are missing practice because you have to, not because you skipped class and hung-out with your boyfriend and now you are behind the 8 ball. If she goes to the West Coast and takes an athletic scholarship, THE COACH OWNS HER! PERIOD! Most coaches can care less about GPA, as long as the team's APR is solid and each member of the team's GPA is above 2.0. Ivy coaches do not share that POV.
If you are a slotted recruit, first or second on the recruit list, you are basically in, and that goes for NESCAC and Seven Sisters. Therefore in any given year, eight players are the heart of the team--four years times 2 slotted players--and unless you do not meet your potential or there is an incredible walk-on, you will play for four years.
Ivies are private schools; the amenities are beyond compare. You are basically at a country club, and NESCAC and Seven Sisters are even better. Unless you are being recruited at Stanford--which I know you are not because you are not American--or USC and Pepperdine--which is absolutely beautiful with dorms on the hill over-looking Malibu Beach--your on-campus experience will not be as elite if you attend a state institution. Just walk through the main part of town at Cal, or UCLA where there are crack houses nearby, and you will know the difference in 60 seconds.
BTW: Most girls go to the school where they are most comfortable with the other members of the team and the coach. A bad recruiting trip can have an adverse effect, even if the academic environment is the best fit. Female athletes are more problematic in this area than male players, who will either choose the better team for many reasons, or the better academics. They will deal with difficult teammates or a coach if they get to start. Period.
If your daughter is not aspiring to go pro, and you can afford the Ivies, that is where she should go. Academically, you may get as much from Cal, UCLA, USC, and Pepperdine, but they don't have the whole package that the Ivies do, nor do they have the cache. With that being said, if your daughter is very independent, driven, and has passion for her academics, than she will succeed anywhere. For comparison, if you play #1 for Harvard, you would play #6 for Stanford. Use that as a guide when comparing all of your options and decide which is the most import factors: academics, participation in tennis or playing in the top three in the line-up, strength of schedule, future in pro tennis or not, Ivy degree vs any West Coast degree that isn't Cal or Stanford.
Good Luck!