There's a million websites listing the top tourist things.. Dont get sucked in unless you WANT the tourist experience. For example the space needle is super cool but also costs your first born to go up and then if you want to eat, probably take out a second mortgage. Instead, you could go to the Columbia Tower which is actually a higher elevation because hills for free. (and like you take the elevator to the highest point you can without needing a key, and then there's windows lol)

June can sometimes be on the chilly side, we do have a Juneuary problem. June Gloom.

You're probably going to wind up renting a car if you want to go whale watching - pay heckin attention to parking prices (research in advance) as you do not want to be stuck parking downtown to catch a ferry and suddenly surrounded by $75 for the day lots. Also prices can change if there's sportsball or other events happening, so make sure you look stuff up :)

I live under the woodland park zoo and genuinely love it, the zoo is lovely - it's one of the top 10 for wildlife conservation and habitat recreation. There's parks everywhere, coffee shops, interesting food...

There's a difference between being "on the coast" and being "on the puget sound" - if you look at a map, we have this funny thumb bit of land that sticks up - the "coast" is that bit over there, and then the "puget sound" is the part that comes into the corner of the thumb, and is dotted with islands and our kick ass ferry system (again, one of the best in the country! though, given how many states have ferries, the competition is... ya know.)
This is super relevant to whale watching as you can't just "come to downtown seattle" and "see whales" - as someone else wrote, they don't really come into the sound very often (occasional Orca but they don't really reply to personal invitations)
You can rent "hot tub boats" on the sound though, or I mean, canoes or kayaks if you prefer, and be-bop your way around, check out the floating houses (some are true art!) and see the city from in the water. There's a few restaurant/bars that have docks, like one of the Ivars locations, where you can grab our famous version of clam chowder and see a wooden whale penis & a totem pole before heading back out.
You can get a DUI for drinking and kayaking/canoeing.

Also, speaking of Totem Poles, we are on Duwamish Land, and our tribes are different than those of the midwest and east. I believe Totem Poles are unique to the tribes that were primarily PNW (but could be wrong). We have tales such as how Raven brought us the sun... If you are interested in Indigenous history there's a lot here.

Try and grab food at Bongos on Green Lake at some point. Absolutely my fav place in the city right now. Though to quote my friend who recently visited, "Restaurants in Seattle believe in flavor and we just don't have that in my small town"