@Dalinar That’s a great question. Because “star” can be defined in various ways, this explanation is a little rambling and centers on how you can possibly pick the profs that are right for you.
I think your question is rather sophisticated, because most people in doing their research on colleges barely get past the USN&WR rankings to determine quality overall. That ranking system IMHO is so flawed as to be almost useless. For example, if you choose Ranked 1 School because you’re guessing that it will have the best department in X, without looking deeper, you might find that a) that school doesn’t have that department or it’s rudimentary. Or b) if it does, the department is run badly. Yes this does happen at the Ivies and elsewhere. There may be Famous Great Prof from 1948, legend in his (or her) time but who hasn’t produced any new research since then and may also be a terrible teacher. Rambling presentation. Still reading directly from notes on yellow pads, the whole thing. And the TAs are the ones really teaching the course. Often TAs are great, but the students are learning from grad students maybe two years ahead of them in studies, in reality . … they may be the “best” TAs in the world, but they would not likely be what you signed up for. You worked hard to be taught by Famous Great Professor who turned out to be not so great after all. Meanwhile in School Ranked #48 or #65 you may have Amazing Young Professor who’s tearing up your discipline of interest because she’s approaching things from outside of the norm. That lower ranked school may well be the best school for you.
If possible look at your department(s) of choice and look through the list of professors. See what their research topics are. Do any of those topics interest you?
Although hugely flawed, it’s not a terrible thing to look at Rank my Professor to see if the dept. profs trend down or up. Beware though becuase people ranking profs there are often the highly motivated, either highly motivated to punish profs or to reward profs, so it’s extremely inaccurate, but nonetheless can give SOME information.
Download the faculty CVs and see how active they are: Do they speak around the country/world often? On what topics? Does that sound rigorous (they’re being named to research posts in other countries or they are asked to give plenary addresses to the major conferences or they guest lecture often in places that seem to matter) or does it sound like they are attempting to become TV-level or Pop-culture level “public intellectuals” (which seems to be a trend in academics currently. They could be both! But sadly sometimes the most “famous” prof in the lay-person’s world can often not be that productive at a school and may not be a great teacher). Check to see when they published papers last. Are those the most rigorous peer-reviewed journals? Or are those journals some of the “we will publish anything if you pay” journals that are cropping up like mushrooms? Are the profs helping their students also publish (maybe that researcher’s name is at the end of 15 names on a paper (exaggeration). The last name is often the name of the funding researcher and they are allowing their students and other collaborating colleagues to publish using their data). Does the researcher have active labs? Has an active grant? Runs a “center” or “program”? How active is that Center or Program (has it hosted an event recently? What else does it do?)
Check to see when the last time Your Favorite Professors taught. Sometimes they have “bought out” of their teaching with grant money so that they could concentrate on their research. Small LACs have less of this (because while they do have research, teaching tends to be emphasized in LACs and in some borders on private tutorials, and in research Us the research takes precedence often over teaching) and I think the UCs have sometimes not allowed this to happen, but I don’t know the current rules. How big are those classes? Does that size suit you?
Some schools, like MIT and Yale, put entire classes online for free. Look at them and see if you like them. Check Coursera and other MOOCs to see if your school of choice offers classes. That is just one indication of many about quality.
Looking at these factors may help you determine the quality of a department and the slate of profs and may help you decide which school is best for you.