'Away' does not imply direction. You could be stationary, not in a vehicle or on a road or path, and used the word 'away' in this sentence.
'Ahead' and 'down' both imply continuing in the direction you are already going. They could also be used when someone is gesturing in a particular direction.
Some people use 'down' for anything further along a path or road. Some people only use 'down' when going south or down hill, use 'up' for north or up hill, and use along for east/west/flat.
It would be unusual to say "I bet there's a rest stop a couple of miles down".
It would be more common to day "I bet there's a rest stop a couple of miles further down" or "I bet there's a rest stop a couple of miles down the road."