they call themselves an "ivy of the south" just like stanford calls itself "ivy of the west" but its not an ivy. if you go around in college educated circles talking about you go to an ivy league school then say duke they're gonna look at you like

then

then
remember the ivy league was created as a sports league, not necessarily for elite education purposes. there are better schools that arent in the ivy league (like Stanford) and mediocre schools in the ivy league (like Cornell).
schools from best to worst in the ivy league (my opinion only): Harvard, Princeton, Yale, Dartmouth, Columbia, UPenn, Brown, Cornell. Studying CS at any of those schools will give you a top tier education, though. as for the black experience I can only really comment on the one I went to. The african-american community is highly intellectual at all of them, as expected. The schools try very hard to be diversified. Manage your expectations, though. Going to a school in a big city will be better than one in the boonies, as a black person. But I wouldnt be too hung up on it either way. You'll find your friends, you'll have a good time,
you wont experience much overt racism (remember these are all educated people) but most of the white kids come from rich white neighborhoods so they really dont know many black people wherever they came from. Lots of kids from NYC though too, who do.
Just go to the best school you can, get your degree, then live your life with a good job and good connections