I'm not sure of what all is going on in Spokane on any given week but I would have to imagine you can find some info through the Inland Northwest Flyerz on Facebook as well as the Disc Golf Uprising (for events specific to Camp Sekani).
There's always weekly League with the North Idaho Disc Golf Club: 1st, 3rd, and 5th Wed. of each month are at Corbin and 2nd and 4th Wed. are at Cherry Hill. There are fees associated with it but is cheaper for NIDGC members. Lots of information at Rapid Fire Plastics in Post Falls.
Mondays are at stimpi ridge. $10 to play acepot included. Tuesdays are SDGA random draw doubles(spokane disc golf association). Weekly rounds alternates between highbridge and downriver, but i think soon we're just going to have them all at downriver. Attendance at highbridge days are much lower compared to downriver days. $5 to play, $6 with the acepot. Wednesdays are north Idaho weekly at corbin or cherry. I believe its $10 to play out there with the acepot included. Thursdays is DG Uprising random doubles at sekani. $10 to play acepot included. Fridays is SDGA random draw doubles again at downriver or Highbridge. $5 to play, $6 with acepot. Saturdays is league at Farragut. They run it in the mornings. Not sure if its weekly or monthly. They post about it on the Flyerz page.
All the weekly doubles start at 5:30 to allow people getting off work at 5 to get there in time. Show up with your cash in hand and you will be welcomed at all weeklys.
Join the Inland Northwest Flyerz and DG Uprising groups on facebook. mostly everything is posted up there for the spokane area as far as weeklys and tournaments.