Well, US Vice President Joe Biden is from Delaware, which helped give us some recognition! :D Newark is a great place to live, I especially love the walkable down town area. Northern Delaware meets South Eastern Pennsylvania and Southern New Jersey, and this is called the Tri-State Area, which is covered by Philadelphia TV News Stations. Our newspaper is The News Journal (Delaware Online) but Newark has its own, The Newark Post, I think.
Public transportation is very good in Newark. There are plenty of DART bus connections and when school is in session, the university shuttles are free to students as well as the public. Amtrak Rail Service runs from Newark south toward Baltimore and DC, and north to Philadelphia and New York City. A newly expanded local commuter train operates from Newark/Wilmington to Philadelphia.
Delawareans refer to secondary roads by name and you can identify an out-of-stater because they tend to use the route numbers. ie: Concord Pike is 202 to a Pennsylvania resident. :D
Local food favourites are the breakfast meat (as already mentioned) called Scrapple, sliced and grilled till it's crispy on the outside. Another local favourite: Single serving packaged baked goods from TastyKake, which can be found in supermarkets and convenience stores. Speaking of convenience stores, as already mentioned, WAWA is king! There you can stop for gas, get very good fresh take-out food like soups, salads, breakfast and lunch sandwiches, a decent cup of coffee, and use a clean rest room. Service is quick and friendly. Their corporate headquarters is based in - where else? Wawa, Pennsylvania. For coffee shops, try a Brew Ha Ha. If you're into Natural Foods, check out the Newark Whole Foods Coop and Cafe on Main Street. If you join, you get a member discount. Otherwise, the number one supermarket is ShopRite, surpassing Acme in recent years.
Delaware State Parks are very nice. I'm partial to Cape Henlopen at the beach in southern Delaware. There's a daily entrance fee for State Parks, or you can purchase a yearly pass/sticker. For a nice day trip or weekender, I recommend heading out to Lancaster County, Pennsylvania (Amish Country), when the weather gets warm.
Newark has its own Police Force and your local hospital will be Christiana Care in Newark, which I believe has a level I Trauma Center. Johns Hopkins Hospital in Maryland (best in the country) and Hospital of the University of Pennsylvania in Philadelphia are within driving distance should you ever need a second opinion or sub-specialty care and hopefully you won't need them. But it's nice to live in a place where you have so many great healthcare options. Good luck with the move, and welcome!