My storage is full and there's so many nice things to pick up. Is there a safe place I can drop things off at where they will be accessable later on? What I'm looking for is something like Diablo 2's "stash"...
There is no shared stash that's accessible from every city. However, if you drop items in places such as in your apartment, or in one of the hotel rooms in the Hung Hua hotel, such as the room with Mei, they will remain there should you revisit that area in a later part of the game.
Most of the time, I've found that its worth it just to sell whatever you don't need and keep it as spare cash to buy stuff later. There's plenty of goodies to be found everywhere if you explore enough and you can find most weapons multiple times.