Hotels in Southern Spain

I don't know what you consider moderately priced but I stayed at the Hotel Opera in Madrid- steps away from a Metro station, and within walking distance to the Royal Palace and the main plaza.
In Cordoba- loved the NH Amistad Cordoba. I did take a taxi from the train station to get here, but right in the heart of it all. Great breakfast room and buffet.
Seville- stayed at a very small wonderful hotel that is in the RS guidebook - Hotel MAESTRANZA . No breakfast but reasonably priced, neat, and old world charm with a modern bath. Very close to everything, walked everywhere from here, but did take a taxi from the train station to get to it.

Last year we stayed at the Hotel Amadeus in Seville and we just loved it. The hotel has a wonderful ambience with musical intruments everywhere and beautiful music playing all the time. They also have a rooftop cafe and tables with knockout views. We bought supplies at local shops and ate lunches of bread, cheese and wine while soaking up the early spring sun from the roof. The hotel is in a great location, a short walk from most sights.

In Granada we splurged and stayed at the Alhambra Palace. It's basically right next to the Alhambra. Rooms were great and views were also wonderful. Nothing beats looking out over Granada at night as the lights of the city twinkle below. The only caveat is that breakfasts are very expensive so I would recommend walking down the hill to the city proper to eat at a local cafe.

In Madrid you can't beat the Artrip Hotel. Hands down the best service we ever had at a hotel anywhere. We walked there from the train station. The neighborhood is vibrant and many sights are walkable.

While we were in Seville we rented a car for a day and drove to Arcos. Arcos is a nnice little town but not sure it was worth the trip. I certainly would not recommend spending the night there. We also took a day trip to Toledo by train from Madrid. Toledo is a must see and people say it's very nice at night after the tourists leave but we chose to go back to Madrid so we could travel light.

Sounds like you have a great itinerary. Have fun!

Madrid - Hostal Acapulco. We have stayed here four times and have always been satisfied. Mright down the street from the metro and very close to Puerta del Sol area and not far from Plaza Mayor.
Sevilla - I also can recommend Hotel Maestranza.
Cordoba- we stayed at Hotel Maestre. This is a hotel, a hostal and apartments. We had a good experience there in a big triple but I was noticing that the reviews on TA are all over the place.

I found the following hotels well located, comfortably furnished and fantastic value :
Madrid http://en.suitesviena.com/
Cordoba http://www.hhposadadevallina.es/en/
Sevilla http://hotelsimonsevilla.com/web/html/en_index.html