Finalizing the itinerary

I highly recommend stopping at Collioure, France which is not far. It has an art history, castle on a hill, waterfront location, charming town.

I would not recommend option 1, seems too complicated for just a few days, you can find all of what you are looking for and more staying in Spain. So I'd do option 2 or 3.

In between Barcelona and Valencia, is the Costa Dorada (https://www.spain.info/en/region/costa-dorada/), one can use Tarragona as a base to explore the region like:

Garraf - laid back beach community just south of Barcelona. Popular with locals and with good seafood restaurants. There is also here a beach house designed by none other than Antoni Gaudí!

Poblet Royal Monastery - a UNESCO World Heritage Site and still active 12th-century Cistercian monastery. It was a fortified medieval royal residence and contains the unique hanging tombs of the old Kings of Aragon.

Tarragona - ancient seaside town with very good Roman ruins, including an amphitheater, intact aqueduct, and Praetorium Tower, was once the capital of Roman Hispania (modern-day Spain). Tarragona's medieval old town is a delight to explore too.

Les Ferreres Aqueduct - Roman Aqueduct you can walk on top of, a few km from Tarragona.

Sitges - the quintessential posh beach town, 30 min south from Barcelona. Has multiple small sandy beaches. Sitges also has nice historic centre lined with boutique restaurants and shops.

Castillo de Miravet - A large riverside stronghold built by the Knights Templar with commanding views of the countryside. The adjacent medieval village spills down the cliff towards the rivers. A great place to bicycle, kayak, or take a leisurely boat down the Ebro river.

If you would like to visit the Pyrenees Mountains, there are a plethora of options to chose from.

From Barcelona, one can take the regional R3 train to the Pyrenees mountain town of Ribes de Freser and then switch to the rack railway up to the Vall de Núria sanctuary for some amazing hiking for the day.

Another option is Vielha, the capital of it's own autonomous community called Aran, which is tucked away in the corner of Catalonia. From there it's a short drive to the Vall de Boí, which is a mountain valley with many old 1000+ year Romanesque Churches, Vall de Boí is designated a UNESCO World Heritage Site. It makes for a good base to explore the nearby Aigüestortes National Park too.

Further afield in neighboring Aragon is Jaca, which is the old medieval capital of the Kingdom of Aragon and is dominated by a huge 16th-century star fortress. From Jaca, you can do a day trip to the Castillo de Loarre (about 1 hr), which is one of the oldest castles in Spain or explore the southern foothills of the Pyrenees.

ViaMichelin estimates the pure driving time for the loop you've laid out at nearly 10 hours if you go only as far as Perpignan, or 11 hours if you push on to Narbonne. That's with no stops, no navigational miscues, no traffic tie-ups, no looking for parking and no time at car-rental agencies. It seems like an awful lot of time in transit to me.

I wonder whether your itinerary already includes Girona? I'd choose it over Narbonne or Perpignan, and it's on the way to Figueres. Nothing wrong with Narbonne or Perpignan themselves; I'm just questioning the geography and timing. Perpignan has a non-touristy scruffiness about that I found appealing. I suspect many tourists would prefer Narbonne. Perpignan has the interesting Palais des Rois des Majorque, though.

Andorra-la-Vella is said to have taken on the look of an outlet mall. (I haven't been there since the 1970s.) I hope one of our other posters can suggest a different place to head for the Pyrenees experience. I know this topic has come up before.

I'm not a beach-lover (especially not a lover of European beaches), so I can't help there, but for sure there are beach spots on the Spanish side of the border, including in or near Cadaques.

Thanks for all the good ideas! Appreciate it very much.