I think that the region of Extremadura, just west of Madrid, will fit the bill. Should be lovely in April too, with rolling green hills, fields of wildflowers, and groves of oak trees.
Extremadura is often overlooked and really underappreciated, in my opinion, it's one of Spain’s most fascinating regions. It's full of time-warped old towns, castles, monasteries, and beautiful countryside, and was the homeland of many Conquistadors. And also the best Jamon Iberico in all of Spain comes from this region!
You can fly in to Madrid, pick up a car, then head west into Extremadura. I'd recommend these places
Cáceres (home base): The old town of Cáceres is a UNESCO World Heritage Site and has a mix of Roman, Islamic, Gothic, and Renaissance styles.
Parque Nacional de Monfragüe: Day trip from Cáceres to this biosphere reserve, includes stunning cliffs & rock formation, plus many kinds of wildlife (especially noted for its Griffon vultures). Has some really great hiking trials.
Trujillo: This town is where some of Spain’s most famous(infamous) conquistadors came from. The town has a few baroque and Renaissance palaces and an interesting Museum of Francisco Pizarro, who led the expedition that conquered the Inca Empire.
Guadalupe: Has the beautiful Real Monasterio de Guadalupe. You can tour this monastery and its collection of art, jewels, illuminated manuscripts. You can also see two cloisters, one late-14th-century Mudéjar, the other Gothic.
Mérida (home base): Mérida is the provincial capital and has some of the best Roman ruins in Spain.
Zafra: On the way to Zafra stop by Castillo de Feria, an originally Moorish hilltop fort. Zafra itself is a white walled town nicknamed "Little Sevilla" and feels very "Moorish".
Jerez de los Caballeros: A very picturesque small town. The old town is surrounded by a Moorish wall with six gates. After it was conquered from the Moors, the town was transferred to the Knights Templar, who left their own architectural mark.
Monesterio: an unassuming little town that produces some best Jamón ibérico in all of Spain. You can find the real Museo del Jamón there, not those touristy ones you will find in Madrid.
At the end you can drive down to Sevilla, drop off your car, spend a few days in the city, before taking the AVE high speed train back to Madrid to fly out.