I found two good properties to stay in in Cordoba. These include:
Amistad Hotel Cordoba, Plaza de Maimonides 3: A part of NH Hotels, this is where I stayed on my first visit. It is a good hotel that is well-located on the edge of the Juderia.
Las Casas de la Juderia Cordoba, Thomas Conde 10: I also checked out this branch of the well-known Seville Hotel. It had lovely gardens and again was in a good location in the Juderia.
Other hotels getting good reviews include Casa de los Azulejos, Hotel Hospes Palacio del Bailio, known for its great design, and Balcon de Cordoba.