Attending college is still a major force in upward mobility for children with parents in the bottom quintile of income to reach the top quintile of income. A recent working paper from NBER looked at the role of colleges in explaining upward mobility outcomes.
Looking at the top 10 colleges for upward mobility in the US I was surprised to see my alma mater Pace University (which also happens to be one of the only for-profit schools on the list) and SUNY Stonybrook (roughly 20 minutes from where I grew up).