Perhaps states out West like Wyoming, Colorado, and Alaska would go Libertarian first. States like that have an independent streak to begin with. I'm sure some Northeastern states like New Hampshire and Maine would be within reach for the Libertarians.
Here is my map (using Independent "green" for Libertarian):
Democrats: 235 electoral votes
Republicans: 181 electoral votes
Libertarians: 122 electoral votes
I understand this scenario to be the first presidential election in which the Libertarians get a boost. They might not win on their first try, but they could very well win their next election in the national spotlight by building on their relatively successful showing as a third-party.