The venue just north and east is 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. The actual neighborhood the park is in is called Sandpoint. Other close neighborhoods include Laurelhurst, Revenna, Lake City, and Wedgewood. 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.
My Favorite Seattle Hotel
This place is DOPE! It is right in the heart of downtown Seattle. Use the code "CC1" to get a sweet rate.