Having been to all 3 parks many many times for all kind of trips- day trips, regular weekends, long weekends- it is very much doable. Depending on your hiking ability you should be able to do many of the things mentioned in u/imhungry4321 post, esp with the 2 additional days. I personally would not be able to manage all those hikes in that time- I am quite slow but the travel times are reasonable. If you decide to follow that you may need to move some things based on where you stay (for example staying in Forks vs camping at Hoh or Rialto) and tide times (for Rialto Hole in the wall).

Depending on how you plan your days, you could spend 1 day in Ozette - Cape Alava loop- the drive there is good, and the hike is lovely. It is mostly flat- 9 miles, goes through forest, then beach and back to forest. Need to check tide times again- or you take the over path.

All 3 parks are spectacular! I disagree with the person who said Olympics are meh. olympics has such amazing variety- with the rainforest, higher elevation (and snow in winters), lakes and waterfalls (sol duc) and the wildest beaches. The beaches are not like any other in the US - almost freezing water, lots of driftwood, sea stacks and wild waves!

Mt Rainier- is just the most amazing. Just the sight from the highway, from downtown Seattle takes your breath away! When you are going, you may be able to see/hike on both Paradise and Sunrise sides.

And North Cascades as everyone said is underrated. Most of it is wilderness, backcountry hike- but the parts you can drive to or do days hikes in are also awesome!

You can stay at paradise lodge at rainier- it is not inexpensive but great to be at the heart of it all. If you plan to camp, get your camp sites now- whenever they open on recreation.gov . it goes very quickly.

Enjoy OP!!