It looks like the NEBR (National Bureau of Economic Research) does a lot of interesting work, and it seems to have a strong MIT affiliation. I applied for a job as an economic research assistant for MIT professor David Autor, who is a labor economist and will be the Associate Department Head of the MIT Economics Department in the fall. He studies the income distributions and skills of workers, amongst other things, and he gave me some career advice.
He advised me to apply to more interdisciplinary public policy graduate programs rather than straight economics programs if I were to apply this year. He strongly recommended working in a developing country on an experimental program through the Poverty Action Lab for a year before applying to economics PhD programs. Now I have a lot of leads to follow, and it's really exciting.