From this answer I understand that it important to get into a top schools with top graduate programs because of the large number of higher quality peers makes a big difference.
I am wondering how do I find those schools? Do I need to look into this list R1: Doctoral Universities – Very high research activity.
I am also under the assumption that some schools have a good graduate program on very specific areas that won't show up in the above list. Where do I find those schools?
Yes, in the US, start with the list you link to. A lot of them are large State funded universities and they have large faculties and most of them cover most fields. But to narrow it to a single field you need to do some research yourself.
They will all have websites listing faculty by department. Some of them also list graduate students. Find departments with a fairly large number of members and then narrow it further by looking at the sub fields and, especially, the recent papers that the faculty has published. But, unless your desired field of study is very esoteric, most large R1 universities and even some R2 places will serve you well. Smaller places can be excellent, but they may also be a bit spotty in the research fields they are able to support well.
