Speaking of 42nd Street: that was the classic Broadway play I saw with my middle son, at a matinee. Lion King, Hairspray, Rent are long-running choices. Alternatively, you may want to see the play du jour.
Broadway plays are expensive; for tips on saving $, see Broadway Discount Tickets 101 at About.com's site for New York City for Visitors.
Note however, that even if you get a 50% discount on tickets -- at say, the popular [link url=http://gonyc.about.com/cs/discountbroadway/a/tktsbooth.htm]last-minute ticket booth at Times Square[/link]-- your bill will still be considerable: yes, the tickets are half-price, but the price they're half of is $120. Also, choice plays sell out fast at the TKTS booths.
Another option is simply to head to a theater and buy cheap seats. Even high up "in the gods" the view will probably be fine, and price can be as low as 30 bucks.
photo © Teresa Plowright