There are no colleges or universities in Chelsea. The best you can do for post-secondary education in the town of Wappinger is Dutchess Community College, which does have a satellite campus in Wappingers Falls in the same building complex as the DMV off of Route 9 (it's called DCC South). Elsewhere, Vassar College is probably about 15 to 20 minutes from Chelsea, depending on traffic, Marist College is probably about the same, and Dutchess Community College's main campus is also probably a similar distance.
On the other side of the river, you've got Mount Saint Mary College in Newburgh, which might be about the same drive as all the others.