There are a lot of historical landmarks in the City of Poughkeepsie; in the town, I can't come up with too many. I know that Poughkeepsie was at one point the New York State capital and that New York ratified the Constitution in Poughkeepsie. The city also has places like the Glebe House, which is a popular elementary school field trip destination. Vassar College (in the town) is also in some ways a historical landmark, because that plot of land was originally bought several hundred years ago.
If you're looking for something flashier like Washington's Headquarters, there's one in Newburgh on the other side of the river.