The influence of Hamilton the musical has started to become very pronounced at this current point in time. As a result of the fact that this is the case, a lot of theater scenes outside of Broadway are reproducing it in their own ways, and a lot of these adaptations are actually surprisingly decent if you were to give them a chance. That said, you should realize that watching these adaptations off of Broadway rather than on it would only give you a pale imitation of the real thing rather than being something that is all that worthwhile.
If you want to go and watch Hamilton in a musical theatre, the best way to go about doing so would be to make absolutely sure that you are watching the play with the original cast. The people that were originally cast in this play really managed to bring the characters to life in a way that would astound you, and as if that wasn’t already enough you will notice that their characterizations are very spirited as well to the point where they would blur the lines between themselves as well as the characters that they have been chosen to play at that precise moment.
While an off Broadway version of Hamilton is probably going to give you a relatively decent time if you give it a try, it would not help you to understand the main reason why this play managed to get so much traction in the world. The original cast have beautiful voices that you cannot compare to amateurs, so spending a bit of extra money to see it is something that you should most definitely try to do.