I'm not from the spokane area anymore but I lived on the east side and fished every chance I could get for over 20 years.......

If you want big browns you may want to include eastern oregon on your list of entrees.... Wickiup Lake, East Lake, and Lake Paulina (near bend) are good big brown trout waters.........

way to many good rainbow and cutthroat lakes near spokane to mention, but if you fly fish, you will definitely want to check out Amber early and often.....

Will also want to get to know lake Roosevelt...

good fishing there for big kokanee and rainbows.. lots of water and lots of fish.....

for lunkers you'll want to start learning the secrets of Rufus Woods lake (the columbia river reservoir below Roosevelt lake)... the lunkers here arn't brown trout though, they are what we call "triploid Rainbows".... a normal rainbow in most respects but genetically modified to make it grow bigger and stronger......

there's also some good fishing for big winter run steelhead and salmon in the columbia and Snake rivers south and west of you......