Nighttime photography is a lot of fun to do, but you'll need a tripod to assist you. Jacksonville has some of the most beautiful locations to photograph. The photographs are especially awesome and breathtaking during this particular phase of the moon and with a clear sky. The light being reflected back to Earth from the moon cuts down on the exposure time greatly as compared to a cloudy or very dark night.
Many great landscape photographs can be shot at night. The color and tone values are deeply enriched. However, there are several things to think about since you will be using long exposures times. Be sure your lens is clean. Obviously you will need a sturdy tripod. Try to be away from bright lights such as street lights in the foreground as the light from those sources will burn out during long exposure times. The composition rules apply to nighttime photography the same as in daytime shots.
You'll find that the auto-focus on your camera will not work as well as it does during the day. Use either manual focus, set your focus setting to infinity or focus on the moon which will give you an infinity reading and then recompose your photograph. A small flashlight comes in handy during nighttime photography to help you find and see the controls on the camera.
For shooting landscapes with a full moon with direct light try a 30 second exposure with f-3.5. Then adjust as needed. Remember doubling the time is only a one stop difference. So if your photograph was too dark to open up one stop you will need a 60 second exposure. A one stop difference if the 60 second exposure was not enough would then be 120 seconds and so on.
If your initial 30 second exposure was over exposed the better option would be to stop down the aperture a stop or as needed instead of shortening the time. Once you get around f-8 or f-11 then use shortening the time by halves.
Adjusting the exposure during night photography will give you creative and interesting light so there is no right or wrong here. You can make a photograph look very much like the nighttime or you can make it appear as if it was in the daylight.
Remember the light from the moon while at different angles in the sky will affect your exposure times as well as the shadows. Also the lower the ISO setting the less grain and digital noise will be in the photograph.
A tip for photographing the moon is the "sunny 16" rule. Set your aperture at f-16 and your shutter speed accordingly to match your ISO setting. Example - if your ISO is 1/100 use 125th of a second. If the ISO is 200, use 1/200th of a second and so forth.