Spain itinerary - 1 week

Hi guys!

Me and my bf are going to ​Spain for almost a week, end of April.

We are arriving at Barcelona airport Sunday 11am, and our flight back is on Friday at 8pm.

We've never been to Spain before so we'd like some help on how to plan our trip.

A few days in Barcelona and then is it worth going anywhere else in the short time we have, perhaps to some "calmer" location? Day trips or even overnight trips? ​We ideally do not want to rent a car.

Thanks