Cornell has larger population of transfer students than other school, because of that, they also do a better job integrating transfer students. Ithaca is not a big city, but it is a vibrant college town. They have a very good economics department, as well as a business school.
Both of my kids like big city (they are now living in NYC), and they loved their 4 years at Cornell. As mentioned by others, Northwestern, Chicago, Columbia are all good choices. You may want to consider NYU too if you are considering Columbia. You should just cast a wide net and see where you get in.
My older daughter studied abroad in Sydney and she had similar experience as you (everyone went to private school and knew each other). She was miserable the first 2 months, but did finally break into their social circle. 10 years later, she is still friends with many of them (going to each others weddings). My younger daughter studied abroad in London and had good experience there.