Chile was great when I was there about a year and a half ago, albeit by car rather than bike; most beautiful place I've been, particularly Patagonia (if you catch the right weather), and quite safe. The Motoaventura folks are good to deal with, though I can't comment on their bikes (I was hoping to rent a bike, but ran out of time).
I would recommend the Atacama Desert and Patagonia over the Lake District where Motoaventura are based; it's a long ride through Argentina if you want to get to Patagonia from the Lake District....