the number for fairbanks is 865 544 3090. I've never been in there, but from what i've seen, it's more of a coffee house/bistro restaurant than a bar. I dunno the age restrictions, but i doubt it's 21+. The website address is www.thefairbanks.net .
As for the grey eagle, I've been there twice and it's by far the coolest venue I've ever seen a band. I went when i was 16 and again when i was 17, and i don't remember any kinds of age restrictions, though I was with my parents both times. It's a non-smoking restaurant type place that really values live music. It's possible that it'll be all ages, and if it isn't i'm sure it won't be more than 18.
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