Rjean makes a good point, you could potentiality spend 10 nights in Catalonia and really get to know the region, then fly direct to Portugal from Barcelona. That would be a good way to hang with the locals and go off the beaten path. I would recommend you do something like this:
Fly in to Barcelona
Barcelona (3 nights) - only focus on Barcelona city sights
Rent car and drive south to
Tarragona (3 nights) - explore southern Catalonia with a car
Use AP 7 to go around Barcelona, drive up to
Girona (3 nights) - explore northern Catalonia with a car
Drive back down to Barcelona/drop off car
Barcelona (1 night)
Fly to Lisboa
Off the beaten path sights around Southern Catalonia, with Tarragona as a home base:
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.
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.
Peñíscola - With its cobbled streets and whitewashed houses, the old town of Peñíscola sits on a big rock that juts out into the sea. The town is dominated by a large Knights Templar castle that looks like something out of the Crusades. Recently, Peñíscola was used as a filming location in the T.V. series Game of Thrones.
Matarraña - nicknamed the "Tuscany of Spain", this area sits right on the border of Aragon and Catalonia. Rolling green hills, lazy rivers, medieval castles, and ancient groves of olives, almonds, and vinyards. There are many old castles towns in the region with Alcañiz being the largest one.
Off the beaten path sights around Northern Catalonia, with Girona as a home base:
Empúries - right on the Costa Brava, this is the site of an Ancient Greek Colony, from the 5 century BC, it was later conquered as a Roman city, but old Greek quarter ruins remains, there is a very good museum on site with artifacts found at the site.
Tossa de Mar - the Jewel of the Costa Brava, a beach town very popular with locals, there is a medieval town with a castle overlooking the turquoise waters of the beach.
Vall de Núria and Queralbs - Vall de Núria is a hiking area in the Pyrenees popular with locals, it's the site of the Nuria medieval pilgrimage. You park in Queralbs, a very pleasant medieval stone village at the base of the mountain, and take the rack railway up about 30 mins.
Ripoll - medieval town in the foothills of Pyrenees, on the way to Nuria, this is where is located the ancient monastery of Santa Maria de Ripoll, where the legendary founder of the count of Barcelona is buried, Wilfred the Hairy.
Rupit, Pals, and Besalú - very quaint medieval stone villages around northern Catalonia, each with their own flavour, my favourite is Ruipt, there is a very good restaurant there called Restaurant Albert, which serves the hardy mountain cuisine of the area.
Vic - ancient market town in the heartland of Catalonia, known for it's intact Ancient Roman Temple and painted Cathedral. Try to be there on the Saturday market day, which is a huge farmer's market on the Placa Major. Vic is known for it's amazing Fuet sausages.