How exciting! I just hiked ~50 miles around Olympic a few weeks ago and it is gorgeous--you're in for a treat! We didn't do any throughhikes, but we did do the Seven Lakes Basin loop hike--if you decide not to do the through hike, I'd highly recommend this one. Go counterclockwise, stop for a night at Deer Lake and another at Love Lake, that will give you tons of time to explore the surrounding lakes and gorgeous views around both camping areas!

Hiking from Elwha should be nice; after hiking to Hurricane Ridge we took part of a side trail that goes down to Elwha for 6 miles (only went a mile or so). It was off the beaten path and beautiful. Hopefully some folks will be able to provide input on trail conditions since there aren't many recent AllTrails reviews for you to work with. 

If you have time, I recommend getting out to the ocean part of the park for at least one overnight. We had a great low tide to explore the sea stacks, but were jealous of all the folks who enjoyed a quiet night tenting right on the beach. Hope you have a terrific time!