Great to hear you're coming to the Tar Heel State. The outer banks are a superb place to bird. Pea Island has some great fresh and salt water ponds that are great for seeing all sorts of water fowl and wading birds. Not sure how many water fowl you'll see that time of year, but it will be good. Just head south on highway 12 and it's on the right after you cross the Bonner Bridge. Cape Hatteras National Seashore is a gem of course. The northern end of Ocracoke is your best and most accessible spot to find Piping Plovers, Wilson Plovers, migrating Semipalmated plovers and a host of other shore birds. North Carolina is one of the few (maybe the only?) places with both breeding and wintering populations of the threatened Piping Plover (it's threatened on the East Coast, endangered else where). The North end of ocracoke is really good for seeing them. If you can make it to Cape Lookout National Seashore, it is worth the hassle. There are no bridges and no roads to the Island, so you will get the full barrier island experience when you come. South Core island is more accessible and less buggy than North Core. Ophelia Inlet on the North is a great place to see migrating birds and breeders. The Cape has a large and currently active Waterbird colony, containing Least Terns, Common Terns, Gull-billed Terns and Black Skimmers. To get to South Core, You'll have to Take a ferry from Ocracoke to Cedar Island. This is a 2.5 hour ferry and is really nice. Then drive to davis and take a private ferry over. you'll need a four wheel drive vehicle, or try to get someone to drop you off at the inlet and pick you up a few hours later. If you don't have a vehicle, the cape is a short, but good walk from the visitor's center near the lighthouse. Access to that area is gained by taking a ferry from Harkers Island. There is a beach taxi that will take you to the cape and pick you up on the half hour when ever you are ready.
Croatan National Forest has Red-cockaded woodpeckers, the only cooperative breeding woodpeckers in NA. They are awesome to watch and the Long leaf pine savannah they live in is a real treat to visit.
Have fun, there is not shortage of good birding sites in the Eastern Half of the State, and the weather might not be so hot in September, although it can really roast in September.