I think the best way is to put them in the museum, or if you do not have enough space in the museum you could wrap them in presents then drop them in the museum. That way they won't count as items (so you could fill up every space instead of normal maximum of 40 items), but then you would not know which pic is which.
I have the villagers who left that are really special to me (one from tt accident, and another that I had a hard time letting go of) in my house. Then there are pictures of all my current villagers (my dreamies) in my mule character's house.
I just put mine by the door. I really just want that feeling of accomplishment of getting a not-real friend of giving me their picture for some reason. SarcasmSoGoodYouDontEvenKnowItsThere