The eastern shore rocks for cycling! I did a 4-day tour there in May, and it was beautiful. Many roads have nice bike lanes, they're clean and debris-free, except for the occasional road-kill, and it was flat flat flat. But I did find the headwinds to be exceptionally strong--maybe they can serve as your hills. LOL I especially found riding in the Blackwater NWR fun and interesting, so you might want to check that out if you haven't already.

If you have a good LBS, someone there might be willing to show you how to change a flat, if you go on a day when they're not too busy--usually mid-week. Also, check out the resources already mentioned, and it wouldn't be a bad idea to invest in a beginner's book on bike maintenance.

Welcome to TE!