-NYC to Boston via chinatown bus (uber cheap) is approximately 4-6 hrs (could be 3.5 hrs on good day)
-NYC to DC via chinatown bus is approximately 3-4 hrs
Based on your preliminary plan, I would suggest landing in DC first and then make your way up to NYC and then Boston.
Here's a problem with Rochester (RIT). It is far. I mean reallyyyy far. It's 6-7 hours from either NYC or Boston. I'm not sure how are you gonna get there. Fellow ADers! help chime in suggestion for this issue. If you did make it to RIT, don't forget to stop by our infamous Niagara Falls afterward! It's only 1-2 hrs away. After that... I suppose you could fly home from Buffalo, NY.
if the weather pattern follows the past - I normally don't recommend visitors to come during Jan on eastern coast. It's incredibly cold. seriously ungodly cold. It can make your trip very unpleasant and unpredictable due to snow storm, blizzard, ice storm, etc. I would say - come on late February or March. But if you wanna live like a New Yorker, then sure come in Jan. we'll man you up