ANC has an outpost of FAI-based Silver Gulch brewing.

I think Humpy's at ANC (concourse B) has a good local craft beer list with a wide selection. Their downtown outpost does, anyway, but it's been awhile since I've paid attention to the airport one. (ETA: confirmed: they have 16 crafts on tap plus 4 macros, and the majority of crafts are local.)

The Alaska lounge at ANC usually has at least a couple of items on tap from Alaskan Brewing (based in JNU), which is a solid craft brewery (the largest, though not nearly the best, in AK), and a couple of other (usually also local) options. I think most of the other Alaska lounges (SEA, PDX, LAX) have at least one Alaskan Brewing (usually Amber) on tap.