Are there any colleges or universities near Dover?

Not really. On the western side of Dutchess County in Poughkeepsie/Hyde Park, you have Dutchess Community College, Marist College, and Vassar College (and throw in the Culinary Institute of America for good measure). You're almost certainly looking at more than a half-hour drive to get to any of them from Dover. On the Connecticut side, there are a few other local universities like Western Connecticut but I can't imagine they're any closer.