The Ixchel Textile Museum and the Popl Vuh Archaeological Museum are across from each other at Universidad Francisco Marroquín, both lovely, and only about 20 minutes from the airport if traffic is ok. That's doable but the airport has been crazy our last 2 flights home so that might be pushing it - depends on your risk tolerance.
It's doable, but I'd be out of the museum no later than 10. But then I have a low risk tolerance.
Why don't you visit the Museo de Arqueología y Etnología instead? It's in the museum/zoo/park campus right by the airport. I haven't been there but others on this forum have recommended it.
Within a 20 minute walk from the airport is a collection of things to do including the Archaeological Museum (which has an ethnology section with textile/clothing exhibits which you might be interested in.)
There is also a botanical garden, a children's museum, a natural history museum, the city zoo, and a good size craft and handiwork market where you can purchase fairly high quality Guatemalan souvenirs and gifts.
I have made this walk several times when I had layovers at the airport. It is an easy walk passing the old equestrian racetrack stands but if you are worried about the time, you can easily take a five minute taxi to or from, or both.
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