This time of year it's about conditions at the dive sites, not just chilly weather on shore. The (Good)offshore dive sites are usually a pretty good distance out and sea conditions are unfavorable. There is not much in the way of shore diving in NC as there are no reef structures to speak of. Ledges/Wrecks/Artificial reefs are the normal sites, all in distances from shore measured in miles not fin kicks.
even during the summer conditions here can change drastically and frequently. It is not uncommon to have charters blown out for weather/sea conditions.
Aquatic safaris in Wilmington would have been a good choice, they are a great operation and have a charter calendar that updates in real time based on conditions.
Aquatic Safaris - NC Wreck Diving at its best. Specifically check out the charter tab for charter info and scheduling
Discovery Diving in Beaufort is also a good choice
Discovery Diving Co.- NC's Diving Headquarters - Discovery Diving Co. they have a calendar on their site also and had trips going out during the week through November.
That being said though you can find groups going out this time of year, not easily and they are usually on standby for conditions. You might find better luck with some of the smaller independent operators rather than the LDSs during this time of year if you want to go during the week.
bletso: I think you may be mistaken in that you are thinking Jacksonville, FL where the OP was wanting info on Jacksonville, NC.