I am planning a trip in mid May for 2 adults to Seattle - Portland - Olympic national Park. We plan to spend about 4 nights in each city and 2 nights at Quinalt lodge in the park. Suggestions about things to see, itinerary, amount of time needed in each place?

I would suggest looking into Crescent Lake Lodge instead of Quinault. Last summer no activities were allowed on the lake by th Indian tribes-- no boating, kayaking, fishing, etc. Lake Crescent is beautiful , some nice hikes close by, kayak rentals available at the resorts.

It very likely will be cool and rainy.

Haven't been to Quinault in 20 years, but do like Crescent for easy hikes and scenery.
Two night is a minimum for both cities if you're going really appreciate all they have to offer.

I suggest 3 (Portland), 3 (ONP) and 3 (Seattle) as you will want some time to explore the ONP and not just the driving days.

As for what to do it depends on what your interests are. But here are a few suggestions:

In Portland, you could go wine tasting in Willamette Valley one day, shop in the Pearl District, visit Portland Saturday Market, OMSI, go to Powell's, visit the International Rose Garden, Lan Su Chinese Garden and Portland Japanese Garden, and have fun with food trucks.

In Seattle, visit Pike Place Market, Space Needle and Pacific Science Center, explore Fremont, ride bikes or take a ferry, Experience Music Project, SAM, walk the waterfront, go wine tasting in nearby Woodinville. Take a day trip to Mt. Rainier.

In both cities you can eat really well, lots of great dining options but start a separate thread.

When we stayed at Quinault, we played in the lake (swimming), took a really cool guided tour of the rain forest from the lodge, did a day trip to the Beaches (Second, Third, Rialto and Ruby) and enjoyed lunch at Kalaloch. And played horseshoes on the lawn.

The Boeing factory tour is amazing, it's about 30 minutes away. You literally are walking above the production line of the dreamliner and the tour is very organized. If you are already doing 2-3 days of nature, then skip the Mt Ranier trip this time. Go to the locks on a week-end, so you can see the salmon jump but also because seeing the pleasure boats and fishing vessels fill the locks is quite good.(I don't know what time of year the salmon are at the locks, though). The Chahouli garden just below the space needle is beautiful, try to go during the week due to crowds. A short ferry ride, with lunch on the other side or at Pikes Market upon your return is a great half day.