I admit to being mystified by the value proposition of Nest thermostats. I have a simple programmable thermostat that I can put on a set schedule (and change if I'm going out of town and want to set everything for energy savings) and the incremental value of having something more dynamic just seems miniscule.
If you only have one thermostat getting a "smart" one doesn't really add much unless you live alone and want to take advantage of the presence features (it knows when you're home) in order to save some money.
However, if you have more than one thermostat (e.g. separate downstairs and upstairs air conditioning/heating) having a "smart" thermostat is awesome! I can change the temperature on both from my phone without having to go upstairs.
We also installed the additional sensors in various rooms in the house so I can control which zone gets used in determining the whole-house temperature (there's often several degrees variation between rooms in my house on hot summer days). The thermostats in my home were installed in terrible locations that don't reflect the temperature in places where people actually are so the remote sensors are fantastic.
I installed a Nest so I could add a remote temperature sensor in my bedroom. I configured the nest to heat based on the bedroom temperature at night and the living room (where the thermostat was) during the day.
Before the Nest, the bedroom would get way too hot at night because it was better insulated than the living room, making it difficult to sleep. Afterwards this was no longer a problem. Saved a bunch of energy too.
Other "smart" tech: remote controlled outlets, later swapped for hue bulbs, let me flip all four of my living room lamps on from the entry way OR the hallway. Before, there was no switch at the entry way leaving me fumbling through the dark for the wall switch at the other side of the room to turn the ceiling light on. Then I'd have to turn the floor/table lamps on/off individually.
