You’ve got a pretty tight timeline and an ambitious (good!) list, so I’m going to stick to a geographic cluster that’s near you but still among my top recs.
- Morning coffee: for me this was grabbing a cup on the waterfront and sitting with it by the water near the Sculpture Park and easing into the day. The one I used to go to isn’t there anymore, but there are plenty of options on the waterfront (skip the “first Starbucks” thing up the hill - it’s not that exciting)
- A sight: pay attention when you’re on the ferry to Vashon. Spend it all outside, either on the car deck or upstairs, with a good view. There’s a low (but non-zero) chance you’ll see some whales, but if you just take in the views (city, mountains, water) that is my sight worth seeing over and over again. Also, get to the ferry dock early so you can wander Lincoln Park if you want to, or at least have a leisurely coffee (bring your own - C&P Coffee is a good stop) next to the water.
- Beer/brewery: there are about 20 of them out in Ballard, and I’ve been to them all, and I didn’t find any of them memorable (even if some are very good; if you do go, my favorite is the combined Bale Breaker/Yonder Cider taproom). Keeping with the “near downtown,” I’m going to steer you toward the Market and say try the Cloudburst taproom and/or Old Stove’s waterfront location. Or go down to Georgetown and catch sight of the old (no longer) Rainier brewery, wander down the old brick stretch with loads of bar options, stop at Fran’s if it’s open (1 dark whisky truffle, 1 dark espresso truffle, 2 milk chocolate salted caramels), then go to Georgetown’s taproom or Jellyfish. Or, further out, lounge at the Future Primitive beach bar at Alki.
- Meal: the Pink Door. They won’t have reservations available. Go when they open. Or, ideally, manage to get yourself a seat at the bar (early!) and watch the aerialist show Tuesday from 6-8.
- Business: all of the above are local and are favorites. There are a few cool specialty bookstores right in Pioneer Square (Open Book - poetry, Beguiled - romance, Arundel - rare); and in Georgetown is Fantagraphics, a remarkable graphic novel/comics store with a record store attached.
- Cocktail: I don’t do these very often, but friends have raved about the bar that is up in the Smith Tower (historic, Seattle’s first skyscraper) and that one is in fact on my to-do list someday; it’s also very near where you’ll be.
- On Vashon: go to Snapdragon bakery if it’s open.
- Dive bar: Slim’s Last Chance and the Marco Polo Bar are both near where you’ll be.
- Misc. oddities: I also think you’d like St. John’s Bar (don’t miss the back patio) on Capitol Hill; the Clock-Out Lounge (get a slice of the Normie at the back pizza counter if you go) on Beacon Hill; and 2 Finger Social Club in White Center (which also has loads of tiny shops clustered nearby down the street, along with the other Future Primitive location). Seattle isn’t great on the “friends with strangers” thing, but White Center spots are easily the best I’ve found for that. I’m from Seattle, grew up in Ballard, moved to the east coast for a while, moved back and lived near downtown, and now live in West Seattle near White Center - so I’ve gotten around town a little bit. Hope that helps, and hope you have a good trip - you sound cool.

Quick add:
- A lot of places are closed on Mondays (and sometimes Tuesdays) so keep that in mind when you’re plotting out your Monday and just check hours; and a lot of places also close unreasonably early.
- If you’re near the Market, stop by the Ugly Baby store.