I live in NYC and just googled the ABD trip, itinerary and tour. i would really hesitate to dedicate your limited time and that kind of money to that tour - I think you could have a much more enjoyable, authentic and personalized trip on your own and save a ton of money OR invest that money in amazing, worthwhile and customized experiences.
Regarding Wicked, since it's a must-do for you, I would buy the tickets in advance - if you are even remotely considering spending all this cash on that tour, don't risk saving such a relatively small amount of money on the chance of a discounted seat.
I also wouldn't just recommend going with the hotel ABD recommends either - I'd really make a list of what you want to do, look at where those places are in the city, their opening hours, and then target the most convenient area for a hotel.
I completely get that you trust Disney and ABD based on your prior experiences. I am sure they put on a good program in NYC, but Disney is definitely not the best authority on NYC and it is super easy to manage on your own. There are amazing, amazing cultural institutions, museums, parks, productions and experiences to be had here. There are fantastic art history and gallery tours, cultural museums, walking tours, tasting tours, musical venues, unique shops, restaurants, sporting events, etc. Depending on your budget and interests you can spend a fortune or next to nothing for a huge variety of activities that match your interests. What types of things do you and your daughter enjoy and what time of year are you planning to come?