There is gonna be a shit tone amount of people on Rainier. If you do go there, go there on a weekday super early (like 6-7am). I highly suggest going up to Camp Muir if you are in decent shape. but check conditions before you go because you might need microspikes or crampons.

Olympic is huge. If you want to visit the Hoh and hurricane ridge, and hike, that is 2 whole days of driving (not counting from Hoh back to Seattle). Olympic is a must visit.

Instead of Mt St Helens (which you can't hike to the peak without a permit), consider parts of the Cascades that's closer to Seattle. All NFs in Washington are amazing. North Cascades NP is absolutely heaven if you are into alpine views. Of course there is always the Enchantment. If you are in super shape the doing that in a day (backpacking permit is a tough lottery) might be one of the best day hike in the US.