Hey there! I did my undergrad at Brown University and got into both Columbia and Yale for MPH programs. To be frank, the Ivy brand helps A LOT with job hunting. In truth the education may not be substantially more different than going to U Washington or UCLA but the networking and job placement potential will vary significantly.
I, and many of my friends who went to ivies, had a significantly easier time getting jobs than friends of ours who went to public universities. Moreover, the ivies have a lot of connections in prestigious organizations so its much easier to get your foot in the door at locations where you would like to see yourself developing a long term career. At 25 I know folks who work in the WHO, CDC, and NIH - a benefit I got from networking at Brown. Heck, I already had an internship lined up at the CDC had I decided to go to Emory because of an alum I met at Brown who works at the CDC.
I think the biggest question to ask yourself is whether you see yourself working locally or not. For example, if you live in Boston and plan on working long term in public health in Boston then it doesn't matter whether you go to Tufts, BU, or Harvard for your MPH. All three schools are very well known in the area. However, if you see yourself moving around a lot and traveling I would say the Harvard name has more reputation and recognition than Tufts or BU and would make it easier to get you jobs - you're also more likely to connect with high level staff because they were alums from Harvard.
