The private courses in Coeur d'Alene include Gozzer Ranch, Black Rock, and Rock Creek Idaho which are all well worth playing if you can get the access. From a public perspective I like Circling Raven the most and then the next course that gets a lot of attention is Coeur d'Alene Resort which has very memorable par 3s and great conditions. A hour and a half north in Sandpoint is The Idaho Club which is one of the toughest courses from the tips you'll encounter. It is a Nicklaus design that was headed to auction earlier this year so I don't know if the course is operating or not at this point. 10 miles north of Coeur d'Alene is Avondale which isn't a bad track if you are set on staying in the area.
40 miles west of Coeur d'Alene in Spokane there are a couple of the best values I've come across with Indian Canyon and The Creek at Qualchan. Indian Canyon is an old course carved through huge pines trees and featuring quite a bit of movement in the property. Qualchan was built in the early 90s I believe and features several memorable holes and to this day remains my favorite course under $30 that I've played. Water comes into play on several holes and I really enjoy the setting. MeadowWood is a county owned course and is solid too. On the private side, Manito and Spokane CC are the main options. They are both nice but not necessarily any better than the public options so if you don't have access it isn't a big deal.
If you head over to Gamble Sands, then your two best options of something to pair with it are Bear Mountain in Chelan and Desert Canyon in Orondo. It's been some years since I've been out there so I can't vouch for the conditions, but they are both within an hour of Gamble Sands to the south.