Where should I place the C wire?
You've identified the mains supply wires feeding the transformer's primary -- the black and the white wires marked L1 and L2 (the latter is actually better labeled neutral). The label on the transformer is visible (PRI 120V).
The two transformer secondary wires aren't visible in the photo. They are two of the three wires that need to go to the thermostat. You should be able to see these secondary wires coming off the transformer and one of them already connected through to the red or the white thermostat wire. The other transformer secondary wire is your C wire.
I have a hunch that your R and W wires may be reversed. R is the one that should go to the transformer's secondary. With the old thermostat the positions of R and W didn't matter, but with the Nest thermostat it does matter. If you do find that W connects to the transformer and R disappears elsewhere then simply swap the two.
Edit: Additional info in a comment confirms the R and W are backwards according to modern convention. Try the following:

Swap the R and W thermostat wires -- R would connect to the yellow transformer secondary; W would connect to a bundle of stuff that can't be seen clearly. Maybe the the white-with-blue-stripes wire?
Confirm that the blue wire and the white wire nutted together are the other terminal of the transformer. Visual check is good; voltmeter check for ~26 volts from these to the R-and-yellow set is even better. Add the C wire into the nut with the blue and the white wires.
It wouldn't hurt to do a few manual checks at the thermostat location before attaching the Nest. Confirm ~26 volts from R to C and from R to W. Probably 0 volts from W to C. Finally try shorting R to W. The system should begin its usual heat cycle and continue as long as R and W are held shorted.