In United States, the ones I have heard something nice about, that offer a professional program in Buddhist Studies:
- University of Virginia - Department of Religious Studies. Very strong Indo-Tibetan Buddhism school.
- University of Hawaii - Department of Religion. Very strong Chinese/Japanese Buddhism school.
- Columbia University (New York) - Department of Religion. Strong Indo-Tibetan and Chinese/Japanese Buddhism school.
- Rollins College in Florida - Department of Philosophy and Religion. Buddhist Ethics.
- Naropa University, Colorado. Undergrad school for kids aspiring to grow in Buddhist Studies.
Many large universities in US offer a program in philosophy (or "comparative philosophy") with concentration in buddhist studies. See for example this list from the Tricycle magazine. Buddhist studies further specialize into Early&Theravada Buddhism, Indian-Tibetan Buddhism, and Chinese/Korean/Japanese Buddhism.
In my understanding, the way this (the choice of school for PhD) is usually done is: you find yourself drawn to one of those subfields of buddhist studies and realize that you keep enjoying online articles and published books by a particular professor from a particular college. Then you go to that college and study under that specific professor or one of his/her students. Like, you're definitely supposed to know much of the professor's work before you even show up as potential PhD candidate.
Also note that since studying Buddhism academically involves studying texts, the student at PhD level is expected to know a couple of primary languages (Pali, Sanskrit, Tibetan, Chinese) and a secondary language (usually French, since most early 20th century study of Buddhism was in that language, or perhaps Japanese or Korean if that's what you study).
Which is why you can't simply jump from a Master's in Engineering to a PhD in Buddhism. You need to start at the grad level and get the basic background in languages, history, culture, and philosophies of the geographical area corresponding to your preferred type of Buddhism.
A slightly less academical and more pragmatic approach is to pursue a degree in "Buddhist Ethics". I believe this usually helps avoid getting pigeonholed into a specific geohistorical tradition, and gets a more "applied" perspective on Buddhism, relevant to the real life in the modern society. Buddhist Ethics is something you'd get if you want to practice Buddhist leadership as opposed to doing research and translation.
Finally, if you dream of becoming a professional Buddhist Chaplain (a "priest"), you may want to consider pursuing the Master of Divinity degree. There is one now offered by the Harvard Divinity School and a number of less famous schools such as University of The West in LA and Maitripa College in Portland.