When we were in Skagway a few days ago, we used the Wifi at the brand new public library -- for free. Most Internet cafes will charge you.
We had DH's I-phone with us, and tho phone service was fine, Internet speed was really slow in most ports.
BTW, Skagway is so tiny their library hours are quite limited -- they didn't open til noon but we could still pick up the Wifi outside.