I strongly encourage you to consider A Bronx Tale. I have seen all the shows on your list, and I personally would have a very hard time choosing between Bronx Tale and Anastasia. I love both very much, but for you, I might recommend Bronx Tale more, especially because I see it's not getting much love on this thread.
I rushed the show, and I got a seat in the front row of the center orchestra section. In my opinion, that was a wonderful seat. Sure, I had to look up a lot, but the experience was the single most exhilarating experience I've ever had on Broadway. And all for $39! So please consider this one! Maybe you can watch clips of both shows online and then decide!