Barcelona is beautiful. If you only have a little time there walk the Rambla. You can see a lot in a little bit of time.
Rent a vespa. They are cheap and you can see a lot more of this city with one.
Book well in advance online if possible to see the David. The lines are absolutely insane. The Ponte Vecchia is beautiful. The pizza here is weird.
Gorgeous. The aquarium is really cool there.
Very easy to navigate this town by train. Went to both Herculanium and Pompeii. You can hook up with a guided tour there (maximum 12 people) for 10 Euro.
Rome is very walkable. Book tickets in advance for the Vatican. Crazy long lines to get in.