The venue just north and east of the University District in Seattle. This neighborhood will have the highest concentration of accommodations including lodging, restaurants, and most importantly a Whole Foods and a Chipotle.
Other close neighborhoods include:
These are all within a couple of miles of the venue and great places to search if you are looking for an Air BnB.
Staying downtown is within reason as well. It is about 8 miles, or roughly 20 minutes to the venue from downtown. If you are planning to do more touristy stuff in Seattle outside of the competition this might be a good option.
And finally the Airport is about 20 miles, or 30 minutes away. You will find the most inexpensive hotels in this area. It is about 20 minutes from downtown Seattle.