Just personal opinions.
Stonybrook focus more on the geometric side of algebraic geometry, like complex algebraic geometry, birational geometry. Some important algebraic geometers I know are Lazarsfeld, Schnell, Starr.
IU, compared to SB, focus on more abstract side of algebra, like noncommutative AG this kind of thing. I'm not familiar with this kind of math but my friend told me Larsen is good.
In UCSD, a big name in algebraic geometry is James McKernan. Kedlaya is also quite good, if you like arithmetic geometry. On their webpage(
https://math.ucsd.edu/research/algebra/), there's also a bunch of people in algebra, including a fields medalist, but (same as IU) I'm not familiar with their work.
IMO, if you like algebra with connection to geometry, then SB is definitely a good choice. If you wish to do things abstract or arithmetic, then SD or IU.
