I'm not sure if this can be done but I will ask anyway.
All my users are set up as Registered but every time they upload their pictures, access is given to Everyone. I normally do not have any users that are not Registered. Is their a way to have the default be Registered instead of Everyone?
That's possible with a modification. But if your gallery should be visible just for registered users, I recommend to set the permissions in the group manager accordingly (access level "none" for the guest group).
I already have it set to none. I have on occasion given access to the site to a different group (e.g., my high school graduating class) to their own section and they initially were able to see all the photos until I changed all the existing to "Registered". Thanks for the info.