Chose Portugal!
The weather is nice (In March / April you can actually go to the beach if you're lucky) and the hotels are not full neither expensive since in Portugal they have only 2 days free in that week and not the all week like in Spain. Everybody in Spain takes the week off so you can imagine hotels, restaurants, etc... I would recommend you to fly to Lisbon or Faro. In Lisbon spend 2/3 days in the city, then you can go 1 day to Sintra and visit the beautiful village, the castle, the palace and start you way down the south where you can stay in Sagres (and around) for 2 days and then head to Tavira, an historical city very tranquil and nice in that time of the year.
As I said, the prices in Portugal for accommodation and food are quite cheap and the food is really nice (better than the Spanish in my own opinion).
Useful links:
Portugal Tourism: http://www.visitportugal.com/Cultures/en-US/default.html</a> Algarve Tourism: http://www.visitalgarve.pt/visitalgarve/vEN/</a>
Accommodation:
In Lisbon chose one hotel in the city center (between Marques de Pombal and the downtown). The Residencial Alegria is a nice choice and has a nice situation (around "Principe Real")
In Tavira I highly recommend to stay in Monte do Alamo. Is a beautiful guesthouse (rural tourism), 5 min away from the city center, the historical city of Tavira. Try Rosário's specialties on a dinner warmed by a nice fireplace with a great view over the sea.
Also check:
www.toprural.com</a>
www.booking.com</a>