I am vaguely aware that in some Orthodox communities, there are Women's Rosh Chodesh celebrations. As I do not live in such a community (and in any case am not a woman), I don't really have any idea what goes on in such an event. I imagine there is usually some learning; I have also seen references online to reading Tehillim or special Rosh Chodesh tekhines, but these lack specifics. I have also seen a number of sites that talk about inventing modern Jewish women's rituals, but these mostly seem to be aimed at a non-Orthodox audience.
I don't expect any kind of definitive answer of what should be done -- I assume there is no normative halakha on this -- but it would be very helpful to have a sense of the parameters governing what could be done, or what is typical at such events.