If you want to see a total solar eclipse, you just need to be between the two red lines on that map. As long as you're within there, what we call the "path of totality", you will be able to see a total solar eclipse.
If you are outside of the red lines, you will only see a partial solar eclipse. This map shows what percentage of the sun will be covered the further north or south you are of the line.
Graham County is entirely within the path of totality, so you should see a total solar eclipse. If you're planning to travel, however, it might be too late. Most campgrounds and hotels within the path are already full. If you're already within the path of totality, my recommendation would be to stay put. Travelling on that day, or even that week, will be difficult.
The center of the path of totality will offer the longest viewing for the eclipse. The further from the center, the shorter it will last. The aforementioned map shows timings at different distances from the center. Notice that it also helps to be close longitudinally as well as latitudinally (that may not be a word).