Hmmm... I have two theatre-related items that I'm especially fond of, but neither are strictly Broadway. I got my programme for the West End production of 'Wicked' signed by Idina Menzel, Adam Garcia, Helen Dallimore, Katie Rowley Jones, James Gillan, and Martin Ball, so that's pretty awesome. Especially when I consider its resale value on eBay (which I'd never do, but I like to consider it).
But somewhat pipping it to the post of most favoured item is my vocal selections of 'The Last Five Years', which I got signed by Jason Robert Brown when I cornered him after a talkback session last September. It's better because I love 'The Last Five Years' more than 'Wicked', and he wrote "to Jan, all the best" in it, which packs a greater emotional punch than just a signature on its own. For twenty seconds, my favourite living composer of musical theatre knew my name. :3
Broadway-specific, I do have an 'Aida' Playbill signed by Adam Pascal and Mickey Dolenz, from my very first trip to New York and my very first experience of stage-dooring. That's quite nice too. :3