I pay 1700 for a 2BR on the hill, 1500 with a roommate is crazy. The best way IMO is don't look online. Walk around neighborhoods and call. Places fill up so fast many landlords don't bother to advertise. Random spots in Seattle are sketchy, do your research on a neighborhood before you go. In my spot you might get mugged and you definitely will get your car window smashed, but no one will murder you. Make sure you aren't in one of the more murdery spots. I like the idea of a coffee meetup, sounds fun! Have you tried Victrola? They're my favorite.
That's what the plan is! Aiming for Columbia City, or Beacon Hill if that doesn't work. The former is near some sketchy areas, but I have some friends there and where they are is totally fine and not super duper overpriced. The hill is nuts at all times of day. Victrola is alright, it's good but it's not my favorite. The spot is cool though! Very very very big fan of Milstead & Co., and Slate. Those two in particular always wow me. Do you know them?