Speaking of which, not all items carry over into NG+, and that unfortunately includes unwashed laundry. Also lost are treasure (annoying since I had a massive stack I forgot to sell) and materials (so it'll be a while until I can craft another eternal lockpick, since those don't carry over either.) But since all weapons, armour, and accessories do make the transition, you'll probably have far stronger gear than anything you'll find in a locked chest anyway, at least for quite a while.
All the items you get from S-Links carry over and usually unlock stuff early. I think. Though I'm guessing you need to at least restart the associated links first. So you won't get all fusion types from Strength right away. I haven't really tested this yet. Also, either the Christmas present or V-Day present from romantic S-Links give you better stuff for those links in NG+. But I dated Futaba so it'll be ages until I see how the effects work for myself.
Not really a spoiler, but