How can I calculate when the new moon will be observed from a particular meridian? I have read that Chinese months start on the day on which the new moon is observed from the 120th meridian east.  From this I am assuming that the new moon is observable from there each time and that it doesn't matter where on the meridian you are (although I suppose it's implied you're in the northern hemisphere).

How can I calculate the time at which the moon is new from a particular meridian?
You need an Orrery. Specifically, one that includes Earth’s rotation.

My noting the meridian on the model Earth, you can see how the Earth may be rotated some amount each time the Moon passes on a line between the Earth and Sun.

The wikipedia page gives a formula.  Take the result (given in UT) and apply the timezone offset for the desired longitude.

The same page discusses Lunar calindars and may have the info you are really interested in.