Barcelona:
Be sure to visit the Dali museum in Barcelona and make it to the Citadel park.
The fountain there is something really special.
Gothic quarter is a must.
In all honesty, I'd avoid La Rambla.
Unless you like getting lost, and a romantic walk with your significant other, I would probably avoid Tibidabo (on the mountain.)
The funicular that goes from the marina to the top of montjuic isn't worth the wait.
Oh, oh!!!
If you're looking for romantic, the gardens behind the National Palace at Montjuic are not to be missed!!!
Be prepared to see a whole lot of boobs and possibly naked men at the regular, public beaches in barcelona.