As you can see, I go to the following often-
Fort Monroe Hampton VA - this is a deactivated US Army Coastal Defense fort north of Norfolk VA. All the seagoing traffic going into the Norfolk-Portsmouth-Newport News area go past it. It is free to the public (it is now a combination city/state/national park). Ample free parking is at the public beach access.
Chesapeake Bay Bridge Tunnel, Thimble Shoals Tunnel Rest Stop, Virginia Beach VA - this is the only public rest stop on the combination bridge/tunnel across the mouth of the Chesapeake Bay. This rest stop will be closing for a number of years in October 2017 as a parallel series of tunnels is built. You do have to pay normal tolls (currently $15 per car) to get on the bridge.
Morehead City, NC - This is a small NC State Port in eastern NC. Large ship traffic is light, but their is a fair amount of yacht and fishing vessel traffic. It also is one of the main ports used by the military when shipping out east coast marines (though I have yet to be able to get pictures of that yet). I usually take pictures at either at Fort Macon State Park in Atlantic Beach - ample parking, free. Go to the fort parking lot and across from the main fort is a beach overlook with a covered platform that is nice. Also on US Hwy 70 between Morehead City and Beaufort, there is a NC wildlife landing that you can take some pictures if there is anything there. It is also public/free.
Wilmington, NC - The largest of the NC State Port system. Still, small by international standards. You can pay to park in downtown Wilmington and take one of a number of very nice pay tour boats. Also, approximately one hour past Wilmington, is Southport NC where the mouth of the Cape Fear River is. This is where all the ocean going traffic first comes inland to go to Wilmington. There is some free parking along the town waterfront/boardwalk. Be aware it can be crowded during busy times and was damaged and will need some repairs after Hurricane Matthew. This might limit access.
I am thinking of later in the year of taking a road trip to Florida and trying to hit Cape Canaveral, Key West, and the Tampa area.