Travelwise this might make more sense.

Do you think a couple of nights for each of those cites will be okay (Seville,Cordoba, Granada, and Valencia).

I would have spent some more time especially in Sevilla. Córdoba could be done as a day-trip from Sevilla, 50 min with the high speed AVE train, but I recommend to do at least an overnighter. Córdoba is much more than the main sights, I particularly like the much more local feel area just a little north of the main sights around Plaza de las Tendilaas and Plaza de la Corredera. Fine, traditional tabernas on every corner.

Always updated on Sevilla: http://www.exploreseville.com/
Great recommendations for tapas bars and restaurants by districts: http://azahar-sevilla.com/sevilletapas/#