Weather can be good or bad in DC that time of year. I would stay south and come up the coast, but it is longer by a good bit that way. Adventure Cycling's Southern Tier and Atlantic Coast routes would be a good bet as was already mentioned. Do you really have time to get there? When are you leaving?

Assuming 85 miles per day it would be about 37 days given my route recommendations. 85 miles is possible but tough given the shortness of daylight and the chances for bad weather this time of year.

60 miles per day average is more realistic, but that would be 53 days.

Keep us posted.