I agree with Scudder, I'd say just focus on Madrid or Barcelona or Sevilla for your one week.
With 7 days there is so much to see in and around Barcelona. You can start in Barcelona for 4-5 days, then head to northern Catalonia for 2-3 days, a land dotted with bucolic farmland and old stone medieval towns with the mighty Pyrenees in one side and the turquoise waters of the Costa Brava on the other side. Girona makes for a great base to explore Northern Catalonia. Some of my favourite points of interests in Northern Catalonia:
Girona - An ancient city in northern Catatonia. Has an impressive Cathedral, towering medieval walls, narrow winding streets, and one of the best preserved Jewish Quarters in Europe. Some of the Game of Thrones T.V. series was shot here.
Besalú - Well preserved medieval town showcasing Romanesque and Gothic architecture. The centerpiece is the impressive medieval bridge.
Dalí Museum in Figueres - Extensive collection of Dalí's artwork, from paintings to sculpters and everything in between.
Empúries - which is the site of the ancient ruins of a Greek colony from the 6th–3rd century BC. It's quite unique as the ruins sit right on the Costa Brava overlooking the sea.
Vall de Núria - is a sacred valley in the high Pyrenees, there is a holy sanctuary and old 1930s hotel at the top, plus a small lake and plenty of hiking trails for all aptitudes. Very picturesque and popular with local Catalans. Accessible by rack railway from Queralbs.
Vic - they have a nice farmers' market day on the Placa Major. Vic is known for it's amazing Fuet sausages and the unique Vic Cathedral, a mix of Romanesque, Gothic, Baroque and Neoclassic styles. You can stop by Xarcuteria Solà S.c.p in the center of town to pick up some delicatessen supplies for sandwiches.
While Barcelona during Semana Santa is much more lowkey than other parts of Spain, know that many villages/towns in northern Catalonia do indeed have their own processions and unique celebrations. This could be a great opportunity to see centuries old traditions "in citu", like the medieval Dance of Death in Verges or the Passion Processions in Girona, while having a less crowded homebase in Barcelona.