You can avail yourself of tennis courts, soccer- and baseball-fields and a kids' play area. You can sit and look at joggers and skaters, or you can jog and skate and look at people sitting down. There's a lot of free (or exceedingly cheap) fun to be had around Green Lake, including the one activity that costs nothing at first, but plenty later: Green Lake is a top pick-up spot.
You also mentioned...
Discovery Park, Trivia Night at the Irish Emigrant Pub, and "climbing the camels at the Seattle Asian Art Museum."
