Don. Start with a good map showing township range section from both USFS and BLM, and go to LR2000 in the areas you are interested in. Compare the two and plot out listed claims from LR2000, and any other site that would show claims. Then go to the county recorder and see if any of those are currently filed, as well as any new filings that may not have made LR2000 yet. This will be the busy season as claims have to be refiled by the end of August. Anything not showing up in either BLM or the county recorder is generally available. Bear in mind they have to be on file with the recorder as well as BLM to be a vallid claim. The final chect is with either BLM or USFS (depending on who controls the ground) to see if it has been "withdrawn from mineral entry or location" If withdrawn, that means you can't file a claim on it.
Fast overview of finding out what is out there, and worthwhile to talk to the mineral person in the office of the agency that has the ground, as well as the mineral/claims person in the state BLM office since they do the mining claims for both agencies.