>Let's see: 120 hz = 8.33 milliseconds per oscillation.  If I sample at
twice this, that's 4.33 milliseconds.  sampling at exactly twice is cutting
it fine, so say we sample at four times that's ~2 milliseconds.
>
>I've got enough memory to increase the number of samples, maybe that will
help as well?

This only helps you pick up the noise..
If you want it to go away, you need to narrow your bandwidth, by averaging.

If you take one sample per second, and the sample is an average over the 1S
period, then you won't see any 60 Hz noise.  If you just take a 1uS sample
once a second, then you will get the full value of the 60 hz noise,
wherever in it's waveform you happen to snag it.  An input RC with a long
time constant will work, but you'll have to adjust the time constant
depending on any other requirements in the system.

You could also take multiple samples at some rate that is an integer
multiple of 60 Hz, and mathematically average them. It's important that you
take an integer multiple of samples though, because otherwise you'll be
left with a "stub" of a cycle that won't average out.

It gets stickier if the noise can be amplitude modulated.  Then the
cleanest technique is to average in hardware.

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