I watched two of Broadway musicals live, they were
Hamilton and
Chicago, not so many because I'm not such a great fan of this genre and besides it's really the truth about tickets. They're rather expensive, especially in case of the hits and you need to buy them in advance because they're sold out really fast and usually there are long lines for buying them
However they organize lotteries for some musicals so you can simply win a free ticket but of course considering such great amount of people the chances for this aren't high.
I can recommend you to watch the both musicals I mentioned earlier, what is really the truth about their shows that they're really amazing and if you have such opportunity, don't miss this great experience
Some people say that in case of
Chicago the original movie was better but personally I liked the musical very much, it's a cool story about criminal and celebrities, nice thing for detective genre
https://en.wikipedia.org/wiki/Chicago_(musical). And
Hamilton has a historic plot mixed with r'n'b musical numbers, a very interesting, talented and original show in my opinion, it's on stage now too both with
Chicago. Also I can recommend
Cats,
The Phantom of the Opera and
Aladdin, I saw many positive reviews about them too