A good short first day trip would be up Bath Creek on the north shore of the Pamlico River to the small town of Bath which is nice and quiet. You can anchor or try http://www.bathharbor.com/
If you feel a bit bolder you could put in a long first day and head up the Pungo River and spend the night in Bellhaven, (several marinas there) wander around town in the AM the set sail back to Bath for your second night and then on to Washington on the third day with a short sail.
It can be nice and warm or chilly and windy at the end of the month but the rivers are wide and currents are not strong so it should be an ideal first trip. Enjoy!!