ON STAGE

* THE MIKADO/ PRINCESS IDA

(New York Gilbert & Sullivan Players, Symphony Space): Every year at this time the 21-year-old intrepid group of loyalists mounts two Gilbert & Sullivan operettas, virtually the only large-scale G & S shows produced in New York. This year, the offerings, performed with large casts and a full orchestra, are the rarely performed ``Princess Ida'' and the more popular ``The Mikado.'' The latter production boasts special guest star Steve Allen. ``The Mikado'' runs from Jan. 5 to 15, and ``Princess Ida'' from Jan. 19 to 22.

* HIM

(Joseph Papp Public Theatre, through 1/8): Christopher Walken has written and stars in this play about the effects of tabloid reality. It isn't opening for critics until tonight, only three days before it closes. That isn't a good sign, but the prospect of Walken playing a character inspired by Elvis is a tantalizing one.

* A DOLL'S LIFE

(The York Theatre Company at Saint Peter's Church, through 1/22): One of Hal Prince's biggest Broadway flops was this 1982 show, a musical sequel to Ibsen's ``A Doll's House,'' purporting to tell what happened to Nora after that famous slammed door. The work, with music by Larry Grossman and book and lyrics by the team of Betty Comden and Adolph Green, has been revived by the York Theatre Company, which has made a specialty of chamber-sized revivals of neglected musicals. Unfortunately, despite earnest efforts from everyone concerned and a lot of tinkering by the authors, the musical is still an ill-conceived bore.

* ZOOMAN AND THE SIGN

(Second Stage Theatre, through 1/15): A revival of the 1980 award-winning play by Charles Fuller, who later won a Pulitzer Prize for ``A Soldier's Story.'' The production is uneven, but this play, about a young girl shot to death in a cross-fire between rival gangs and her family's attempts to combat society's apathy towards violence, still packs a wallop. Larry Gilliard Jr. and Tony Todd give standout performances.