Close and near are basically almost the same, but the difference is that near can only mean physical distance, while close can also mean emotional distance, or distance in time ("a close call|).

Away by itself can mean any length ("100 yards away" "two blocks away"), while far is just a long distance. If you meant "far away" it would mean a place that is a long way away, not the distance itself.

Hope this helps.

I am sitting close to the door.

I am sitting near the door.

These two sentences mean the same thing.