Ended up making it! www.24time.co
The code can be found at www.github.com/stopachka/right-time
There's one model called Meeting.
A person chooses a city by interacting with the Places Autocomplete API. When they choose, it returns latLng positions, which are attached to the meeting. As soon as the model has both positions for the cities, it makes an ajax request to /api/meeting, sending the location parameters.
The API returns back all the best times. I'm pretty sure I'm not doing it the ember way though, perhaps the model can be broken down differently, and the times can be models themselves.