Becuase I don't know where you live, this is tough question.
There are no "must-see" colleges out there. I consider "must-see" colleges to be TYPES of colleges..not specific colleges. In order to determine what TYPE of college is a match for your student, it's important to visit various types of schools. I catagorize colleges like this:
Urban college campus - those colleges that are located in a city but DO NOT have a "campus feel"...ie..no dormitory quads, no sprawling lawns, etc. The campus is mixed into a typical city environment. (examples - NYU, GW, College of Charleston)
College within a city - those colleges that are located in a city but have a definitive "college feel/college campus" (examples - Georgetown University, Columbia University, St. John's University, UPenn)
College in a town - Colleges that are located in a small city or town, where the college and campus are a large part of the town, but the town stands on it's own without the campus as well (examples - UVA/Charlottesville, Salisbury University/Salisbury, Wake Forest/Winston Salem,)
Colleges that make the town - Colleges that are located in a semi-remote area where the small town has embraced the college and becomes a college town. (examples - Washington College/Chestertown, University of Oklahoma/Norman, Virginia Tech/Blacksburg)
Colleges in the middle of no-where - Colleges that are un-to themselves. They stand alone, they are a destination and they are independent of a town within walking distance (examples - Lincoln University/Lincoln, PA, Shepherd University/Shepherstown, WV,)
I feel it is important to visit the various types of colleges, so you and your student can determine which type you like and then you can narrow the search to match the profile of the college that "fits" your student. If you student says they want to go to NYU as an example, find a local school that fits the same profile, tour that college. If you student does not like the "city feel" of no campus, the hustle and bustle of traffic lights, cars, ambulances, etc....they won't like NYU, or another urban campus...and you've saved the time and money of going to a far away destination knowing that that TYPE of school is not what your student likes. The same thing applies to size of the campus. One walking tour of a 30,000+ student campus that takes a college student 20 minutes to walk to class...may seem overwhelming...and your student may opt for a smaller campus with less students.
Once you have narrowed down the TYPE of college, then you can narrow down the size and the particular major your child may be interested in. I always feel that type and size are key to the decision. If you student finds the right type of college, they'll be happy at any school they apply to as long as they are all the same type. (if you student is applying to NYU and Shepherd College...they don't know what they want and chances are they will be transferring! 59% of students who start at a 4 year university DO NOT finish AT THAT college...pretty interesting fact.)
I hope I have been of some help to you. Best of luck in your search. Let me know if I can be of any further help.