I would read through the "Top questions about Washington"
I felt a little bit like people in your area would feel if someone said, "I have 4 days to see Ireland and Northern Ireland."
I understand that this is all the time you have available, but you must understand that you will see very little of Washington State in that time.
I would head to Mt Rainier National Park for your day outing that you mentioned. Top tip: leave early in the morning, and I mean 0600 early, to access the park and the parking lots at Paradise before they get too crowded.