I replaced my existing "dumb" thermostat with a nest and it has certainly been worthwhile, both in terms of energy cost savings and in having a convenient, pleasant interface for temperature control.

I purchased the third party Skylark app and installed it on my phone and my wife's phone so that the nest goes into "away" mode only when we are both out of the house. I think the official Nest app also added similar functionality recently.

After this initial set up, and a week or so of "training" we haven't had to think about setting our thermostat. Our house is just magically at the correct temperature when we are there but our bill is lower than it was before we got it.