I wanted to circle back around with a quick report on my 3 nights (2 1/2 days).
I ultimately decided on Burgos for a few reasons - and it was just what I was looking for (although other places probably could have been as well). I opted for a late afternoon bus back to the airport on my final day and a stay at the nearby Hilton just to sleep before my return flight - it has a very nice shuttle.
I took the Alsa bus direct from and back to the airport T4 bus station. The station is well-marked and easy to find from T4 and is very modern with a large nice waiting area, a small cafe, good bathrooms, and good signs for where busses are arriving. From there I took a 3 hour direct bus to the bus station in Burgos. I purchased my tickets online ahead of time. The busses do sell out - before I had fully decided which time I wanted, the earlier bus sold out so I had to wait several hours for a later one. Both busses were either completely or mostly full. It made no stops - I didn’t check a toilet but did see one woman who appeared to head that way.
My hotel was not far from the cathedral and an easy flat 10 min walk from the bus station. The train station is further out (trains didn’t suit my schedule this time).
I was not looking to do a lot of sightseeing, but the cathedral is impressive. The audio guide you can download to your phone was great and the path through the cathedral took me through a large part. I would do a repeat in order to be able to better process the last half. Senior price of €9 was a bargain.
I also went to the Museum of Human Evolution. I had read about it but ultimately decided between it and the Museum of Burgos based on mentions from here. Thank you, Ms. Jo and jaimeelsabio. Senior price of free was a double bargain. Ha! The museum is modern, big, and very well signed with Spanish and English. Especially of interest to me was the bottom floor record and display of findings from the nearby archeological site Atapuerca (which you can see with a guided tour).
Otherwise, I just wandered, ate, and sat by the small river in the beautiful park area. There are interesting places that I didn’t see (these few days were about just being somewhere and relaxing), so I will probably return when I head back to that area with a car in a year or two. Big thanks to dlindstron for advice!
And Zaragoza is definitely on the next-time-longer-trip list!