Dd has done auditions for all sorts of place including the NYT and has just had a couple of offers for drama school (one of which she intends to take up). From what I understand pretty much the same rules apply everywhere:
*Go for something that you could realistically be cast to play- so a character roughly your own age and your own type.
*Try to find a character you can identify with rather than something you think will go down well with the panel.
*Always, always, always read the whole play (so if you buy a book of monologues, source the play for your chosen monologue as well).
*Try to avoid the shouty, ranty and macabre (panels get awfully fed up with murdered babies).
*Try to avoid anything that might conceivably embarrass the panel or seem aimed at a panel member. In one of her first auditions dd did the speech from de Angelis' Jumpy where the girl rants at her mother and ends with the words "I hope you never get laid again; besides, you are too old! TOO OLD!" and apparently one of the panel members, a middle-aged balding man, looked at her and muttered "happens to us all, you know". That interview did not go well.
*Have a good time- most auditions are a good day out, and NYT according to dd are very friendly and make you feel at home.