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It is difficult to say which are the best, but the big names are usually associated with famous universities such as Harvard, Stanford, Johns Hopkins, Mayo Clinic...etc
Nah, there's a definite pecking order in each field, and it's different in each field, and some of the big names actually are pretty mediocre in at least some fields, and quite a few "no names" are bigshots in certain fields. And you have to remember that residencies are hospital based, not school based, so eg you wouldn't be doing residency at "Harvard" per se, you would do your residency at MGH, Brigham, Beth Israel, etc., similarly instead of "Hopkins", you might be doing your residency at Bayside, Sinai, etc. And these places are far from equivalent, even with the same affiliated university. You more or less have to pick a field, and then talk to academic faculty in those fields and get the buzz on which places are strong, weak, malignant, etc. No way you can make a useful list without word of mouth of multiple people you trust, and it won't be a single list across multiple fields.
But for the OP, first, if you are asking about the
least competitive fields, you can pretty much throw out neurosurg and orthopedics from your last question. The folks who are struggling to get an IM slot aren't competitive for these. The best IMGs rarely get these, and when they do, it's after pretty significant US experience and networking. Nor should you really care about what the "best" residency programs are, based on your initial question. The same person asking about less competitive fields should not be asking about the "best". The best program in a noncompetitive field can be very competitive. The person who is competitive for IM generally might not be close to competitive for IM at eg MGH. In fact, the person not competitive for IM at MGH might still be competitive for the "worst" slot in some of the more competitive fields -- there is a lot of overlap.