I would recommend starting with a Benchmark or Gazetteer map book of your desired destination. As a rule of thumb, all NFS and BLM land; unless specifically prohibited, allow dispersed camping up to 14 days. This would be the green areas on your map. If you have questions about specific spots, you should check with whatever district management office is responsible for that particular location.
NPS, DoD, DOE, and NWR sites; although publicly owned, generally do not allow dispersed camping.
State forests are an entirely different animal. You need to check with each one specifically for their rules. Off the top of my head I do not know of many state owned lands (in any state) which allow dispersed camping. Though I'm sure there are some who do. YMMV.
In AK you can basically boondock anywhere as long as it's off the highway enough and it's not private property.