Your best bet is the conductive ink kind of sensor.
These are a little bit pricey but easy to get hold of. Sparkfun have them for $13.
They're pretty easy to use as they act just like a variable resistor, whose resistance changes as you bend it. You can make them into an analogue sensor by adding a fixed resistor. The impedance buffer (an op-amp) is optional, but will result in much better sensor readings, especially as you intend to use fairly long wires to connect the sensor to the Arduino.
The datasheet for the sensor (which you should read) contains lots more suggestions for circuits.
You can stitch a little pocket into clothing and insert the flex sensor. Use them in the fingers of a glove:
Or in a whole dress:
Accuracy: Flex sensors aren't super accurate sensors. They give you a reasonable sense of an amount of bend, but aren't great for precision applications, E.G. robotic teleoperation. I don't know how much accuracy you need for the neck, so it's very hard for me to say whether it's good enough for you. If you want a more accurate sensor, you'll need to specify exactly how accurate.
Robustness: What will kill the sensor is not the angle of the bend, but the minimum bend radius.
The datasheet for the ones at Sparkfun didn't mention a minimum bend radius, but these ones specify 5mm. I.E. you can bend one around a 10mm diameter tube, and they'll be fine. So I would imagine that going round the outside of an elbow would be OK, but the inside would probably pinch the sensor and break it.