Well, all of my gaming experience is from New Castle County, but Delaware is a small state.
I have no idea about gaming groups in the Dover area, although the Dover Air Force base does seem a good option. If you are willing to travel a little bit, the Wilmington/Newark areas have a lot of gamers. It's probably slightly less than an hour's drive from Dover.
As for gaming stores and resources, there aren't a lot downstate. I believe the only significant resource in the Dover area is a comic book store, Superior Comics. I have never been there, so I can't speak of them specifically. Be glad you didn't move to Sussex county where there doesn't seem to be any major stores.
In New Castle County, there are two main stores: the Days of Knights in Newark & Between Books just north of Wilmington proper. I'm friends with both of the owners, so certainly recommend both.
The Days of Knights is mostly devoted to gaming & gift type items (Enchantica Dragons, swords & daggers and such). If you are looking for something in print it may be your best chance. If you can't find something, ask. John (the manager/co-owner) apparently has a lot of out-of-print stuff stored away, although I don't know what his policy is on dipping into it. They also have a games club that is behind the store. There is a lot of room to game there, although it may be full certain nights of the week. If you are looking for miniatures, that's the place to go.
Between Books is a combination store. It's a comic book/book/gaming store. They have the best science fiction/fantasy section I have ever seen in a single store. The gaming section takes up 4 or 5 shelves of product (with a separate one for miniatures & a case of dice/painted miniatures, etc). However, it is all bookended and sorted by publisher. You may have to search through a lot of stuff, but there are a lot of great finds. Much of it is out-of-print. Greg also doesn't believe in marking stuff up. All of his out-of-print comics & gaming stuff is cover price. There is a back table or two in the rear of the store for gaming. I'm not sure what his policy is on using it though.
If you have any questions, feel free to email me.
Glyfair of Glamis