Re: Competitive Fellowships (e.g. surg onc or peds)
Agree with what has been said to look at the alumni of a program and see where they have gone. However, some places will list fellowships gained by their residents without stating they did a post-graduate research fellowship (because they decided late or didn't match the first time). These are not marked with a *.
A possilbe distant substitute for "word of mouth," and a quick and dirty "pre-interview" way to find a solid program in any specialty look at the program's website for graduate chiefs operative experience. They will usually list the last years graduating chief experience by ACGME subtyptes (endo, operative trauma, non-op trauma, vasc, panc, peds, etc). Look for bigger rather than smaller volumes as compared to the ACGME minimum (usually listed as the first row of numbers). ACGME requires 20 pediatric cases. Disclaimer, residents count cases differently (if they scrub, if they dictate, or only if they do the case vs. watch the attending do the case).
Another "pre-interview" way to see about an specialty experience is look at the program's website to see their 5-year plan. Some places you will do specialties such as peds only in your 4th year (R4), or only your 2nd year (R2), and some will have you rotate as a junior resident (R1 and/or R2) and senior resident (R4).
Last, an advantage about going to a program with a fellowship, esp. a university program, they will have easy access to research opportunities which are usually funded. If you have to look for a research opportunity, though it is not hard, it takes time.