What should i do about this problem?

When im talking to people, or even when im just around people i dont know where to look. Like if i look into their eyes, it feels awkward, but if i dont it feels like im being rude. And when im in public i have no idea where to look, the main reason is because i am a fairly noticeable person. I am 6'8", 340lbs with very long shaggy hair and i have a beard, and many people have said i look like a biker. And every time i just space off i accidentally stare at someone, and before i realize im staring at them, the damage is done. Just imagine seeing a man of my description, and you think hes staring you down. So i tend to look up at the ceiling, or just down at the floor. What should i do about this problem.