They should talk to their math faculty first.
It also depends on what they see as their future career. If they want to work in industry, the “prestige” of the program is less important. However, if they are interested in a faculty position, they really need to attend a top-20 program. As to what are considered “top-20”, that is what they need to ask their faculty mentors.
Unlike for undergraduate programs, the ranking of graduate programs is determined within the field.
Here is a good website to help find the right graduate program for them:
They should also check out the Reddit pages for graduate programs (r/gradadmissions), the Grad Cafe (https://forum.thegradcafe.com/).
I’m not certain what the profiles of prospective grad students normally look like, but your kid has a good GPA from a LAC (which are generally considered very reputable), competition prizes and research experience. Many top programs no longer require GRE scores. I don’t know what percentile a 970 would be considered, so I don’t know how good it is.
Your kid should also not limit themselves to programs in the USA. My kid applied to Neuroscience programs abroad (and will be attending a program in Canada).
Good luck to your kid!