From a career pov? imo little to not at all - unless you pick up some useful/relevant experience. So, if you are interested in say IB, they won’t care at all- unless you get an internship with one of them while you are there, or are randomly lucky enough that somebody interviewing you knows somebody who went there. Especially true if you are applying for jobs in the US: your “top Ivy league US college” will tick all the ‘prestige’ boxes.
If you were looking at graduate school I would say potentially, b/c of exposure to a bigger pool of profs to write LoRs, or who might have connections w/ other institutions.