How to Sell Diamonds and Other Items
Just throw them on the floor of your apartment and sell them from the decor customization menu.
Pawn Shops and Black Markets
You can find a pawn shop in the world. Usually in the basements.
There are also some pawn shops available on the ground floors of some buildings – though the ones I’ve found often have inconvenient opening and closing hours, so it’s probably a good idea to find several different stores so one can sell items if they like.
I found 2 places. One with a symbol of books that identified as a pawn shop and one with a symbol of a man holding a sack that identified as black market.