This is my third response from Wicked (I sent a Playbill-request to the cast about two years ago and I sent Lindsay Mendez fan mail when she was in the show) and I am always amazed by the speed and size of the responses! This response took about two weeks, but my second response from Wicked took less than a week.
Overall, I would say that Wicked is probably the best/easiest show on Broadway to send fan mail to. They are by far the most consistent about responding to all fan mail and most of their responses take 2-3 weeks or less. Also, they are the only show on Broadway that will possibly respond to fan mail even if a SASE is not provided. I would still recommend including a SASE when you send things to them, but, if for some reason you cannot (or forget to) send a SASE, Wicked still might respond to you.
So, if you are a first time fan mail-sender and/or you are looking for a guaranteed, quick response, I would definitely recommend sending fan mail to Wicked! If you have any questions about sending fan mail to Wicked LLC or a specific cast member in Wicked, please check out the Wicked page of the site or send me a question through the Ask Me Anything page!