Is there a gift shop in the real one?
They've been slowly rebuilding it over the last 50 years, but it's nowhere near done. It involves figuring out where each and every block goes, often undoing previous reconstructions. You won't be going inside it any time soon.
There are gift shops everywhere, of course, but I highly recommend the one at the Acropolis Museum (at the bottom of the hill). It does a great job of putting the site into historical and archeological context.
Pretty much every shop/business surrounding the Acropolis is a gift shop, they all sell little souvenirs and stuff.