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

Any recommendations?

It's a small detour from your route (20 miles), but *in* the route there's
no such interesting place: Almagro. This village is well known for their
Summer Theater Festival, playing 17C comedies. It has a beautiful Main
Square, pure Castilian, and the Corral de Comedias, the place dating from
the 17C where the comedies are played.

This is the link to the route I propose in ViaMichelin, a very good Europe
route planner (the link is shortened by TinyURL): http://tinyurl.com/28g7a
In the step-by-step itinerary in the page, you'll find links to the tourist
attractions of Almagro and even hotels.

Just an alert: the names of certain roads (mainly expressways/highways,
whatever you call them) have recently changed in Spain and not all the road
signs and not all the names in ViaMichelin have already been changed. So, I
would take more into account the name of the village ViaMichelin heads you
to, than the name of the road.

E.g. at the beginning of the itinerary, taking you out from the airport,
ViaMichelin says:

Head towards Madrid, Zaragoza, Burgos via N-100 for 1.1 miles.

Well, N-100 is no longer N-100 but M-14. But the exit you should take is
still Madrid, Zaragoza, Burgos.