Pac writes:
We plan to use Madrid as our home base for the first 7 days and take day trips to other cities in the region such as Granada, Cordoba, and Sevilla. Are the day trips to each of those three cities feasible -
Spain is a big country! Sevilla is more than 350 mi from Madrid - kind of like Pittsburg from NYC.
You can do Sevilla (2.5 hours by high speed train) and/or Cordoba (1.5 hours by that same train). I think Granada is out of the question for a day trip from Madrid. More realistic Madrid daytrips are Toledo, Segovia and el Escorial.