I stayed at the Seattle Marriott Waterfront hotel last August. Walked to Safeco Field every day for the ball games. It was an easy and pleasant walk. The Renaissance is closer than the Marriott to Century Link Field where the soccer games will be. Century Link Field is next to Safeco Field. The walk is easy. Maybe 15 - 20 minutes. The walk is about 1 mile. It will actually be quicker than time spent waiting for the Light Rail or busses.
If you go to the Marriott Property website, and then to maps and transportaiton, you can enter in a location to calculate the distance between the property and the address entered. It gives you disance and time, just like mapquest or expedia does. Benefit is that you don't need to enter the address of the property as its already populated.
We just returned from a delightful 5 night rewards stay at the Renaissance in downtown Seattle. We were upgraded to a great corner suite on the 25th floor with views of both the Space Needle and Puget Sound. We arrived via the Coast Starlight from LA and the cost of the taxi from the King Street station was $5.50. I would venture to say it is about a 12-15 minute walk to the sports venues from the Renaissance. A warning: Taxi cabs during evening rush hour can cost a lot due to the length of time in covering only one short block. The 'wait time' at 50 cents a minute adds up surprisingly quickly.
Here's another thing: The Renaissance is at the top of a hill, so though walking to the sports venues is downhill...when returning from walking around the downtown area, it is either a gradual ascent or a steep ascent depending on which streets one takes. We found we appreciated getting caught at a signal at the intersections so we could catch our breath without looking like two oldsters huffing and puffing... The location of the Renaissance, though up a hill, allows for great vistas. All the staff members we encountered at the hotel were extremely accommodating and friendly.