4 nights in Barcelona
First, I've flagged your post to get it moved to the Spain/Portugal board.
I see you're new to CH. Welcome! Here's a link with a lot of replies:
If you go to the Spain board and type Barcelona in the little block titled "This Board," you'll get every post where Barcelona is mentioned. After looking those over, besides being hungry :), you may be able to narrow down your choices. "Non-touristy/hidden gems" isn't necessarily a qualifier in my opinion. You'll have great food. Enjoy!