@labrad00dle - Usually, the best way to find out how supportive and nurturing a graduate program is is to ask the current students and very recent graduates (like, within 3 years, but the current students are better and more accessible). The professors in the department will tell you whatever, but the current students will give you the real lowdown. For a student who is really concerned, I would say talk to 2-3 current students from their top 3-5 programs to get the full picture from a couple perspectives. If you take them aside and do a Skype call or a private one-on-one meeting, they’ll be able to be more open and honest (as opposed to a departmentally organized event with a lot of people around, although sometimes they can be honest there too).
This is not often something you can tell at the outset, unless you happen to have a network of alumni of your college who have recently gone to PhD programs in your field. I did, because I was in an undergraduate research training program, so I heard anecdotally from other students who had graduated and started PhDs how good (or bad) they thought their departments were. Usually, a student starts by outlining a reasonable array of programs to apply to on the basis of research fit, reputation and other factors (location, etc.) Then once you’re admitted, you go to visit days and that’s when you start to shape your opinions of the departments.
Undergraduate advisers, interestingly enough, are not necessarily the best people for this task. They often simply don’t know what are the nurturing vs. more independent departments. Some really exceptional advisers make it their business to know. But even recent graduates often don’t communicate the mentorship and advisory struggles they are having to old mentors, so undergrad advisors often know which programs are strong in their area and turn out good scholars - but not necessarily what the departmental style is. (This might be different at research universities, because professors who teach both graduate and undergraduate students may be a little more familiar with other graduate departments in their field and their internal workings. But professors at LACs don’t always know.)
I will also say that an LAC student does not always need a more nurturing department. I went to an LAC and I certainly would not describe my graduate department as nurturing. While I was initially surprised by how hands-off my department was, I quickly came to value that independence. I felt that my LAC had prepared me very well for doing research more independently, and along with the relative lack of oversight came more freedom to determine my own interests, shape my own academic program and basically do what I wanted to do. My PI never made me do anything I didn’t want, and the freedom also meant I could do things like a market research internship one summer (which was directly related to me getting the job I currently have, which I love!) My advisors were generally there when I needed them to be but stayed out of my way when I wanted to do my own thing, which was actually pretty great.
Also, I want to be clear that more independence/freedom/less direct management doesn’t mean totally hands-off, leave-you-to-the-wolves kind of thing. Departments vary a lot, and it’s a spectrum. I think it simply means that the department expects you to be independent much faster than other departments might. Professors also vary, and you can find a supportive mentor in a more hands-off department (or a more hands-off or even neglectful mentor in a normally very nurturing environment).
(I also might advise your daughter to not completely rule out the South, and certainly not to constrain herself to only applying in the Northeast. It’d be great if she could get a PhD in her chosen area, but allowing herself some flexibility in the location of her program increases the chances she finds a good research fit. A great fit at a department with a good reputation may actually give her more location options down the road, particularly if she’s interested in an academic career.)