There are actually two visitors centers in New Bern. One is for the Craven County Convention & Visitors Center which is located Inside the New Bern Convention Center on 203 South Front Street | New Bern, North Carolina 28563 (800) 437-5767
This is the one we went to first. It is right down on the river. This is where I got pamphlets and maps of the town and also recommendations for lunch. The other one is the one for the Tryon Palace Historic Sites & Gardens. Everything here is on the hour and half hour. There is a 20 minute film, there are tours of the George W. Dixon and the John Wright Stanley Houses (the tour starts from the Visitor's Center - a docent takes you), and the tours of the Palace also start on the hour and half hour.
We were too late to see the film - it was ending. So we bought our tickets ($15 each) and walked over to do the noon palace tour. They told us no pictures allowed inside. When we went back we saw the movie (photo 2 and 5) and they also have a model of the various properties (photos 3 and 4).