Yes, there are lots of moose throughout the state. KeepitCold's advice is true. The eastern part of Idaho is good moose hunting grounds; I've seen some nice bulls hunting Palisades for elk as well. Island Park Zone is another great place for moose.
But if N. Idaho has the best odds for non-residents, then let me tell you, there's no shortage of moose. I see moose every time I go out whitetail hunting up there. Mid-September is a good time to come, as they are in the rut, and the calling is primetime.
Here's the thing to weigh out. East Idaho will be more open with sagebrush and aspen stands, and a good bit of thick timber. You can go there, glass easily as they come out in the morning to feed, and then stalk. I think you have a better opportunity to pick and choose in E. Idaho.
In North Idaho, you are more in timbered areas. Glassing is not as easy. But walk down any creek in any drainage, and you'll likely find moose tracks.
Pretty high success rates wherever you decide to go.