2-3 weeks in PNW, April May:
The season eliminates a lot the best country, all the mountain high country.
Definitely go to Mt. Rainier. Stay at a lodge as high on the hill as possible. It it more than a big mountain. It is GINORMOUS! Do whatever day hikes are possible, possibly in the Tatoosh Range which will have great views of the rock pile.
In Seattle, visit Pike street market, all the nearby shops, and go up the Space needle, and ride the monorail. Also visit the shops on the waterfront.
Take the ferry from Seattle to Bainbridge Island, even if just for lunch, and return. Its part of the Seattle experience.
If you hit a stretch of fair weather, an easy trip worth doing is to drive out to Lake Ozette on the Olympic Penninsula, hike 3 miles to the coast on a cedar puncheon sidewalk, camp on the beach. Hike 3 miles south on the beach, inspecting indian carvings in the rocks, and camp on the beach a second night. From there, hike 3 miles back to Lk Ozette, completing a triangle. If the sun is out, you got lucky and it will be spectacular. If it is overcast and misty, that is not unusual, and enjoy it anyway. Check on permit requirements as its a popular hike. Hit the hot springs at Sol Duc on the way back to Seattle.
Visiting Leavenworth is a great diversion. The apple orchards will be blooming and the valleys beautiful. Depending on the snow level, day hikes to Colchuck lake, Stuart Lake, Eight Mile Lake, Rat Lakes, are all good day hikes. Permits are required for overnight stays, I believe.
A great trip would be to drive to Chelan on the East side of the Cascades, take the boat to Shehekin, stay at a bed and breakfast, and do day hikes out of Stehekin. Lake Chelan is a 60 mile long, 1-2 mile wide glacial carved lake. If you want to make a hike out of it, have the boat drop you off at Prince Creek, and walk to Stehekin, which will take about 3 days.