There is a lot more to do and see in Antequera and you are able to visit El Torcal and the wolf park so that would be my choice.
For free parking: Behind the Plaza de Toros, there is the Parque de Maria Cristina and the street is called Paseo de los Colegiales. Beside this street there is the Recinto Ferial (Fair grounds). There is plenty of free parking on the street and the fair grounds. One can walk to Alameda de Andalucia (which is downtown) in 5 minutes.
The parador is a good modern hotel with good food and plenty of free parking.
1. Municipal Museum - Located in the Palace of Najera and has the famous Roman statue of the Ephebe of Antequera.
2. The Alcazaba - A large Moorish fortress from the 14th century.
3. Most Beautiful Churches - The Baroque period was the most prosperous time in Antequera. This list includes the five churches with the most art:
a. Convent of Los Remedios - Calle Infante Fernando.
b. Santo Domingo Church - Plazuela de Santo Domingo, s/n.
c. El Carmen Church - Plaza del Carmen.
d. Real Convent of San Zoilo - Plaza San Zoilo.
e. San Juan de Dios Church - Calle Infante Don Fernando, 67.
5. Antequera Dolmen Sites - an ensemble of megalithic monuments made up of the Menga and Viera dolmens and the tholos of El Romeral.
Best Restaurant: Arte de Cozina (Calle Calzada, 27-29; Tel: 952-840-014).
Dress code for churches: Shorts or bare shoulders are not allowed for either women or men.
Wow. Thanks for all the information. It's great. You've certainly put forward very good reasons to stay. I'm convinced. Thanks for taking the time to post. Much appreciated.