I found the harbour area by far the most interesting. And, it had the best and cheapest paella. There were hotels there, but I am not sure whether they would be up to your standards.
Las Ramblas de Catalunya used to be the best shopping street.Picasso museum is good, it includes early Picassos almost entirely. I liked the Miro museum better...I think it is in the park on the mountaintop.
If you like music, it is important to purchase the LLuis LLach CD called "Enero 76". I think it is called: "Gener '76" in Catalan. That CD has a cultural importance which is unparalleled in Catalunya. Franco died in December 75, and so this CD marks the cultural blossoming which followed. The music is beautiful, too, and the text extremely interesting. LLach declined afterwards.
There is also a stained glass ceiling, one of the most beautiful in Europe or anywhere. Is it in the Radio Building? If this interests you, I will find exactly the name of the building.
The best part of Catalunya is the culture. Go daily to music and arts, and ye shall be fulfilled.