Thank you for your question. One of the most popular areas to go surf fishing is called Cape Point off of Cape Hatteras. You will need a four wheel drive vehicle to get their by driving on the beach. You will want to enter right around Ramp 44. There are other stretches of the beach that you might find more secluded and what you are looking for. There is a 15 mile stretch of beach north of Avon and south of Salvo. Access would be via Ramps 23 - 34.
At the end of the day, because of the variability of what might be running given the time of year and so forth, I would speak to the local bait shop in Avon (or wherever you happen to be staying) and ask them advice for local help. I have always found them to be very accomodating with regard to this information.
For two different fishing reports, check out our fishing page. The second one breaks it down by the type of fishing you are considering and lets you know what's running. On our fish page give you an overview of each type of fish that has been caught on the Outer Banks and when you are likely to see them.