Best place to stay near the University
For two and a half years, we travelled to Seattle to visit our son and his family while he was in a Post Doctoral program. We always stayed at the Silver Cloud because of its location, but also because it is well managed, comfortable and friendly. We visited the hotel during the summer, winter, holidays, busy times and quiet times. 
Here are the positives: 
The rooms are large and well lit, the junior suite is perfect for a family wanting some privacy. 
Fitness center is clean and well maintained.
Pool is very nice.
You can walk to good restaurants and the excellent University Mall.
The Burke-Gilman Trail (biking and hiking) is right next to the hotel!
The front desk staff is always courteous and responsive to any questions or problems.
Complimentary breakfast is a good feature(although see below for a few more comments)
Tuesday evenings they offer a Manager's Reception which is a nice amenity (usually wine, cheese and a few wings)
Free transportation within 3 miles, to the University or the Children's Hospital or even a grocery store (there is a refrigerator in your room).
Negative:
Having stayed at the hotel at least 7 times, and usually for 5 to 7 days at a time, the breakfast got very old. The eggs and the sausages were really bad, I would say nearly inedible. Cereal, muffins, waffles were okay. They would be wise to change out the menu for breakfast every few days.