I'm looking for a way for people to be able to upload photos to my site easily, but allow me to "preview" them before going live on the site.

Any ideas on how to do this/what program to use would be appreciated!

Automatically your going to need a members area. Once you have that you can have a field in the database table that you can set to a value that means it's approved. You could build this yourself or do a Google search for what your need.

If you have a cPanel for your server, there are usually a good handful of Gallery setups in there that you can install. Many/Most of them include the ability to have accounts be created as well as the ability to set up hierarchies of access, permissions, and for approval of uploads etc. Might want to check those out if you have cPanel on your server