Why do you want to see the "true" analog signal ?
Whether you use a "heavy and expensive" transformer, a capacitor, or an optoisolator in between, you'll see some different waveform than what your other mains devices will see.
In my first experiments, I was rather interested in
1) Is the mains signal there?
2) What's the frequency ? ( compared to what my millis() says )
I soon was convinced that pulling the blue N to Arduino GND and the brown L to whatever smart circuit was not a good idea, as you can easily plug in the wrong way.
So forget about the 120V analog signal!
I found a standard optocoupler, which I combined with a reverse biased led and two decent resistors as the very minimal circuit.
In Europe, we have 230V 50Hz, which is equivalent to 325V peak. 150k resistors result in 2mA peak, which is just sufficient to activate led and optocoupler. They take one half wave each and limit the reverse voltage for each other.
The effective power burnt in the 100k resistor is less than its rated 1/4 W. If you want/need (?) a little more current, you might take care about the power rating of your resistors, or have more - smaller ones - in series. And of course, the resistors are not on the breadboard, but directly in the power line, well isolated... edit: How to directly show pic ?