Where is the nearest shopping center, strip mall or regular mall to go to around Dover?

If you're looking for big-box retail shopping, it's a toss-up between the Poughkeepsie Galleria and the Danbury Fair Mall. They are virtually equidistant from Dover -- which is to say, neither one is close. You're talking at least 35-40 minutes to get to either one, maybe more if there's traffic.

There are very small strip malls up and down Route 22 in the general area of Dover, and some on the other side of the Connecticut border, but those aren't really places I'd look for comprehensive shopping.

Your only real option in Dover itself is a supermarket.