nest 2nd gen, no common wire/terminal in the fan coil unit
Add your C wire to the wirenut you see up front

In your photos of the wiring, you'll notice a wirenut that joins orange, purple, and blue wires together.  Joining the blue wire in your thermostat cable with that wirenut will give you a blue C wire at your thermostat.

Why, you may ask? Well, the wire that connects to the green G thermostat wire at the thermostat terminal block goes to one coil terminal on the relay at the bottom (you can just make out the bottom relay's terminal diagram in the bottom photo).  The other coil connection on that relay, then, must connect to C to complete the circuit from transformer, through thermostat switch, through relay coil, and back to the transformer again.  Lo and behold, the other relay coil connection is the orange wire, which goes up into the wirenut in question, which is then connected back to the transformer via the purple wire.

Furthermore, the red R wire at the thermostat terminal block connects to a pair of brown wires there, and one of them runs off to the other transformer terminal, relative to the transformer terminal that the purple wire connects to.  So, we have our C wire connection, in the form of a conveniently placed wirenut even.