schrieb:

~ 9 AM local time. We'd like to get out of Madrid (car rental) and
stop somewhere approximately midpoint between Madrid and Baza, Andalucia
for a rest and rent a hotel/whatever for one evening to become acclimated
to the time change/rest.

I'm seeking suggestions of a nice relaxing place to rest midpoint between
the two locations.

Any recommendations?

Maybe Baeza near Jaen.
http://barnal.de/fun/bilder/london_heathrow_sm.jpg

If you just want landscape for a short rest, you might stop near
DESFILADERO DE DESPEÑAPERROS

http://www.andalucianatural.com/despenaperros/mapa.htm

Regards, ULF