For those of us who live in the area, we know what the biggest draw Delaware has over PA, NJ, and MD. There is no sales tax in Delaware! When it comes to buying large appliances, computers, or other expensive items, Delaware is the place to shop and buy. The two main arteries to shop are Concord Pike (US Rt 202) and Kirkwood Hwy (Rt 2). (There are plenty of other large areas to shop as well.) It would be fruitless to go into much detail because there are hundreds upon hundreds of places to shop, from large chains to specialty stores.
The two largest gathering places are the malls, of course. Concord Mall is on rt 202 near the PA state line and is a run-of-the-mill mall. There is no large food court here, though there is a small gathering of eateries near the north end of the mall. It is anchored by Boscov's, a budget superstore, Strawbridge's, and Sears.
Going south on I-95, about 15 minutes from Concord Mall, is the Christiana Mall. Christiana Mall is fairly large and more asthetically pleasing than Concord. There is a large enough food court with many choices. It is anchored by JC Penney's, Macy's, Lord and Taylor's, and Strawbridge's. The stores here are perhaps slightly more upscale than Concord, but only by a hair. Neither of the malls are intimidating to your wallet any more than other malls around the country.
For antiques, I recommend Rt 52 going north out of Wilmington. There are a couple small towns on the way that have a good handful of antiques and specialty shops.
Rt 13 south of Wilmington is also a very heavy commercial area, but the choices are a bit slimmer and the area just looks kind of worn out. Though crime is not a widespread problem here, it does seem to happen more frequently here than other areas.
For car shopping, Rt 13 south of Wilmington is chock full. Also try Cleveland avenue in Newark at the northwest corner of the state. For luxury vehicles, shop at Pennsylvania Avenue in the city of Wilmington.