Live on LI (about 20 mins from Stony Brook) and spent A LOT of time in Seattle.
I actually love both but seems you have a lot of decent information above. I wouldn't say LI is anti biking especially in SB area, especially if living close to work, but Seattle is more biking friendly like any city really. YOU WILL need a car on LI but depending on where you live, there are towns where you would be able to walk (or bike) to everything you want/need for example Port Jefferson, Babylon, Huntington, Northport but overall a car is necessary.
LI weather is better IMO only because there is less rain, snow, wind but for you, as you indicated, weather won't be an issue in either case. Both are great for travel (plenty of flights), for road trips I think LI is better, once you get off LI, of course. From Stony Brook/Port Jeff area you can even ferry over to CT (with a car) and have easier access to the entire northeast (CT, RI, MA, VT, NH, ME etc). You also have NYC an 60-90 mins away and the east end (wine country north, hamptons, montauk, beaches on the south). Northwest coast is more rocky, cliffs, volcanic and beautiful, LI is relatively flat, greener/trees/hills rocky beachs on the north (where you'd likely be) and flat sandy beaches south.
As for people, I find both to have their pro's and con's but you'll adapt to either. There is probably more diversity in the east overall but both are amazing places IMO. It really comes down to where you get the gig or if you have to choose then do you prefer the northwest or east.