Jon, Much of the public land around Baker City, OR is National Forest. Good info to be found at
https://www.fs.usda.gov/wallowa-whitman
Scroll down to "Eclipse Info". A few good points: since cell phone/internet systems may be overwhelmed, don't rely on apps, carry paper copy maps. Make sure you are totally self-sufficient with all water, gas, food, etc you'll need for your stay. Be patient and leave no trace. NO CAMPFIRES! From a retired US Forest Service officer