Thank you both for the replies.
The few smaller places that I am very interested still have a good infrastructure to do research, and after talking with faculty and residents at these places, I believe that with hard work I could easily get 10+ publications during my time there.
I don't have aspirations to become faculty at a giant academic institution. My interest in academics lays more in teaching (which I have a background in), and creating a sustainable international experience for myself and residents, and less so about being a research giant (although I realize that it's apart of the game).
I mostly wanted to ask those more in the know than I am, about how much the name of where you trained matters for fellowship and a job afterwards. Thus far throughout undergrad and med-school, it doesn't seem to have mattered a ton, but I wanted to know if that would change in the future. More to your point Sparty, the places I felt I fit best were these smaller programs, but before ranking them highly, I wanted to have a complete understanding of the positives and negatives of attending a smaller, less academic, training program.