We rented a car for our 30 days in Spain in 2012. Roads are in good shape, navigating is easy, and our economy diesel got great mileage. Trains are fairly limited in coverage in Spain. If you don't want to drive, assume that some of your travel will best be done using buses - which are fine (and inexpensive).
April is a great time to go because it includes both Easter Week (Semana Santa) and the April Fair in Seville. I would try to include some of both celebrations in your plans, probably a couple of days of April fair in Seville and some Semana Santa elsewhere (my favorite was Holy Thursday in Zaragosa, but Burgos, Valladolid, Salamanca and Santiago de Compostela are probably really good choices too).
Weather will be rainy up toward Santiago de Compostelo in April, but hopefully nice down south. Our route was kind of a figure eight. We started in Barcelona, then Zaragosa, Pamplona, San Sebastian, Burgos, Valladolid, Salamanca, Avila, Segovia, Toledo, Valdepenas, Granada, Ronda, Gibraltar, Tarifa, Cadiz, Jerez, Sevilla, Cordoba, and finally Madrid (plus day stops between on travel days).
I had originally intended three weeks to include Spain and Portugal. Then only Spain because there is so much to see. Then a full month because there is so much to see. I wish I had twice the time because there is so much to see.
I posted a trip report here (Spain: clean toilets, affordable lodging). I talk a little about everything so you may pick up some things that will help.