- Inside the coil.
- Inside the coil plug.
- On the back of the coil socket in the electronic enclosure.
- On the PCB.
- Or combinations of the above.
If you fit the damping resistor inside the coil, this has the advantage that coils can be easily swapped. However, it may prevent the coil from being used on another detector.
Some people have put the resistor inside the coil plug, but quite often this is not practical due to the limited space available.
If you use a multi-pin coil connector, one flexible solution is to put different value damping resistors on the back of the connector. By wiring the appropriate pins together inside the coil plug, different damping resistors can be used with different coils.
Putting the damping resistor on the PCB is probably the least flexible solution, as each coil would need to have similar characteristics.
The solution posted by waltr uses a combination of points 2 and 4 above, and may prove difficult for begineers to implement.
Personally, I've tried all the variations above over the years, and tend to go for point 3 as the easiest and most flexible solution. Keeping the damping resistor out of the coil and the coil connector, allows the same coil to be used on other detectors.

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