Definitely Barcelona
The port is about a 20 minute taxi ride from the airport.
Hotel suggestions
Jazz
SB Diagonal Zero
Hilton Diagonal Mar
Barcelona if sailing on an “ o “ class ship is regarded as day one with Rome ( a minimum 45 minutes transfer time over an hour in heavy traffic ) regarded as interporting,
Be sure to pre book any visitors tickets you may need for Park Guell or La Sagrada Familia.
If you have the time I’d recommend a minimum two or probably three days pre cruise.
Taxis are plentiful and there’s also a very good metro system.