I trailer a Catalina 22 but haven't sailed it on the east coast. However, since you are in NC, have you thought of cruising your own waters or up to the Chesapeake? Lots of folks do cruise the Florida keys, the west coast of Florida and the panhandle. I'm sure there's more water to sail than 1 week will cover in all these places.
You might consider a Chesapeake cruise that takes you to the Boat Show in Annapolis, usually around Columbus Day if I remember correctly.