There is a Military Marina in Norfolk at Joint Base Little Creek. It is a nice marina and generally has some transient space available but like most military marinas its hard to get a monthly slip. You'll need to call first and then before you enter the basin you have to radio (not sure of the channel right now) to get clearance to enter. Don't enter before you get the clearance and don't go the wrong direction inside the basin or a patrolling military small craft may "politely" redirect you. You can call them at (757) 462-7140. I stayed there for our trip from Annapolis down to Beaufort, SC and it a pretty big marina with decent facilities. They also have diesel available there.
If you google the name of the base you may be interested in you can probably find out if they have a marina by typing in something like "Joint Base Little Creek Marina." I think there is one in Jacksonville NC but I believe its far off the ICW and its pretty shallow at low tide. For the Navy anyway, it is normally part of the MWR (Morale, Wellfare, and Recreation) department on the base and if it is not I'm sure MWR can direct you the right way.
As was mentioned before, if you are a member of a Yacht Club somewhere along the ICW that is "friendly enough" to offer space available transient slips to other yacht club members you generally find that they will reciprocate. Its good to have a letter or some info indicating that you are a member of a club and they they allow space available transient stopovers. Its also a good idea to have a few extra club burgees from your club available as most clubs I've visited like to have a display somewhere. Not all clubs are this friendly, but you'll find that most are. There are a few "stuffy" clubs that consider themselves above this but I'd say many don't mind at all and even welcome you in with a drink or two.
In addition, you may want to check out some of the restaurants along the ICW that have docks. Give them a call and some will let you tie up for the night if you eat there (if there is space available). You won't have electrical hookup but then again you'll get a nice dinner with place to tie up without having to anchor out and use your dingy. Take your time and you'll have a pleasant trip. I know my wife and I enjoyed our transit down.
There are some Skipper Bob publications that are very useful and one of them is a guide with all kinds of info on Military Marina's on the Great Loop (which includes of course the ICW). Some of the info may be out of date but its a great start. Skipper Bob has sailed off into the sunset (God rest his soul) but I've found his publications to be very useful guides (not navigation info but chock full of good stuff like phone numbers, contact info, etc). Here is a link to the Skipper Bob site.
http://www.skipperbob.net/publications
Go all the way to the bottom for the FREE Military Marina guide. You may want the Anchorage Guide too even if you don't plan to anchor on your trip. It give you some info in case you get stranded between marinas and need to drop the hook because you're getting ready to run out of daylight.
