What would you do with 1 afternoon in Granada (after the Alhambra in the morning)?

Cathedral de Granada- I would do this but the Albayzin neighborhood is fun to wander if you can find a guide for a walking tour.

A long lunch

I enjoyed the Sacramonte area with the gypsy cave museum. Not sure it is for everyone, but I wanted to see the area unique to Granada. I walked from my hotel near the Alhambra - be aware that the climb to the museum is steep. Going after the Alhambra, I think I would take a taxi from there and then afterwards walk through the neighboring Albayzin area and down toward the Cathedral Lots of great views from the Sacramento area. https://en.granada.info/sacromonte-caves-museum

Musicians in the group? Manuel de Falla's house museum and foundation are very close to the Alhambra. Tour in Spanish with attempts at English when I was there. Still quite interesting for me to see, but quite probably not of interest to those unfamiliar with de Falla's works.
https://en.granada.info/manuel-falla-house-museum https://www.manueldefalla.com/en/foundation

I found the Royal Chapel with Isabella and Ferdinand's tombs moving. https://en.granada.info/royal-chapel I thought the basilica of St John of God was incredible,.much more interesting than the Cathedral. It is in the Cathedral area. https://en.granada.info/basilica-san-juan-dios

Other than the final hills up to the Sacramento cave, I found every where in Granada very walkable. Taxis were also available at the Alhambra. Lots of interesting choices. You won't go wrong going with whatever appeals personally.

My answer is to stay within the Alhambra and see in more detail all the stuff that a half-day tour will gloss over, out of necessity. The Alhambra is IME one of life's peak experiences if savored like a fine wine. Half day, to me, doesn't do it justice.

I, too, spent more than half a day at the Alhambra.

There are many other worthwhile sights in Granada. One that hasn't been mentioned is San Juan de Dios:

photos of (mostly) San Juan de Dios

Another vote for dedicating the whole day to the Alhambra

I mentioned San Juan de Dios in my post above.

The Alhambra official website gives an itinerary suggesting 2.5 hours. Other website seem to suggest between 3 - 5 hours. I found 4 hours with audio guide to be sufficient. The gardens were not in full bloom during my visit. https://www.alhambra.org/en/maps-plans-alhambra.html

OP, I like your idea of having an afternoon itinerary researched. When on site, you can decide if you want more time at the Alhambra or move on to other areas of Granada. There is much to see!

We enjoyed the Royal Chapel of Granada beside the cathedral more than the cathedral itself. Also, wandering the streets from Mirador de San Nicolás back to Plaza Isabel La Católica, along the river and past El Bañuelo / Baños del Nogal. Beside the cathedral is the La Alcaicería, the old silk market.

We (in our 60’s) spent four days in Granada in October with our son and daughter-in-law (in 30’s), upon moving on to our next stop I asked what they liked best. We saw many of incredible areas and sights already given. Alahambra was #1 and our afternoon at https://granada.hammamalandalus.com/ Hamman al Andalus was #2.

Thank you to everyone for your helpful replies! I think I've got a good tentative plan that I can put aside if we want more time at the Alhambra.

What day of the week? If the weekend then hangout and dance in the square with the locals, watch the buskers and the wedding parties. J