Can you tell me a bit more about public history opportunities at Yale that you've heard of? I'm actually leaning toward UCLA because of public history-- they have a cluster of courses in public history, a professor who heads the Autry Museum of the American West, and really great link-ups with museums in the LA area, so I'd be able to get some seriously good experience.
As for pros and cons, I love Los Angeles, I had a wonderful time at UCLA when I visited, there's a wide array of professors I could work with (some of which are great fits for me), there are a lot of public history opportunities, and I really felt good about the department and the kind of work I could do. For Yale, the program is obviously great (and higher ranked than UCLA), they gave me a bit more money, my potential adviser is an incredible fit for my interests... but I honestly do not like New Haven, and the city I live in (and the things I would do outside of graduate school itself) is a very important factor to me.