Seville - You cannot go wrong with Hostal Van Gogh. They also own Hostal Picasso and Hostal Dali.
http://www.grupo-piramide.com/ If you pick the Van Gogh, request a room with a bathroom, because the ground floor shared bathroom is so small, I had to put on my jeans whilst standing on the toilet. But the location cannot be beat. From the door, you can see the walls of the Real Alcazar and it's literally 1 minute to the Cathedral and 5 minutes walk from Barrio Santa Cruz.
In Madrid, I personally loved Hostal La Plata (
www.hostal-laplata.com ). They are on the Gran Via, steps from the Metro and about 5 minutes walk from Puerta del Sol, El Corte Ingles and great nightlife. Also, the MadridVision, hop-on-hop-off bus tours stop across the street. Another great feature is that although the frontdesk closes, there's a doorman that lets you into the hostal. Traveling with another 20-something girlfriend, I felt safe walking in and being recognized by the doorman.
In Granada, I recommend the Hostal Nuevas Naciones. Cheap, clean, and close enough to the Gran Via for easy access, but far enough away for a good night's sleep.
http://www.granadainfo.com/nuevas/granadahostal.htm Good luck and have a wonderful time!