Hi, Terri. Welcome to Virginia!
We live on the same peninsula with Newport News and Hampton. Newport News is a very long city stretching from the tip of the peninsula at Hampton Roads all the way up about 25 miles, practically to Williamsburg. Sharing the peninsula is the city of Hampton, home of Langley Air Force Base and NASA-Langley. The lone interstate (I-64), intersects the peninsula and takes you to Norfolk to the east across the Hampton Roads Bridge Tunnel (i.e. the parking lot on Friday's during the summer) and to the west leads to Willamsburg and Richmond. Not sure where you'll be staying or what you are interested in, but wherever you want to go, you'll probably have to depend on I-64, which is of course under a perpetual state of construction, so be careful!
If you are interested in a shopping mall, along with several restaurant chains, there is Patrick Henry Mall and Yoder Shopping Center at the intersection of I-64 and Route 238 (Jefferson Ave.) Here you will find many places to eat such as Outback, TGI Fridays, Ruby Tuesdays, etc. A lot depends on where you are staying as to where I would recommend eating; I don't think there are any restaurants on the peninsula I would go out of my way to eat. Ask at the front desk where you are staying and I'm sure they can recommend places close by.
As to places to visit, again it depends on where you are staying and what you are interested in. There is a fine museum in downtown Hampton, the Virginia Air & Space Center, which can be found on Settler's Landing Rd off of I-64. They have excellent displays on the history of Hampton, as well as the history of aeronautical development at NASA-Langley. Plus, there is an IMAX theater, which shows many science related movies; and they will be showing the special IMAX version of Treasure Planet in December! If you like nautical history, there is a very nice museum called the Mariner's Museum at the intersection of Routes 60 (Warwick Blvd.) and 17 (J. Clyde Morris Blvd.) in N. News. Here you will find many exhibits that deal with the shipbuilding industry and other nautical themes. They are working on a special exhibit showcasing pieces of the ironclad Monitor, that has recently been recovered from off of the Carolina coast.
Hope that gives you a couple of ideas, and I would be happy to give you some more info, after I find out when and where you plan on staying. For more up to date info on this area, check out this website:
http://www.hamptonroads.com
Hope you have a safe and enjoyable trip!