Make sure you double check anything listed on the Playbill schedule link provided above. There are quite a few schedule changes, so it is not accurate for your dates. For example, it lists Monday performances for An Act of God and Fish In the Dark. Those shows do NOT have Monday performances while you are in NYC. Good luck!
For Monday night your choices are: Broadway - Wicked, Kinky Boots, Mamma Mia, Phantom Off Broadway - Ave Q, Clinton the Musical, Preludes, Ruthless the Musical Mamma Mia and Phantom have matinees on Thursday. Fish in the Dark has a matinee on Friday if you want to squeeze in another show.
Wow! You're seeing some great shows. Of the 4 possibilities you listed, they are all worthwhile. You can't go wrong with any of them. If I had to rank them, I would probably go: 1.Something Rotten 2. Hand To God 3. Twentieth Century 4. Gentlemen's Guide
We Can Do It and Where Did We Go Right from The Producers The Company Way and Grand Old Ivy from How to Succeed What Causes That from Crazy For You Mine from On The Twentieth Century You've Got What I Need from It's A Bird, It's A Plane, It's Superman Fit As A Fiddle and Moses from Singin' In the Rain
I wouldn't suggest dropping any of the shows you have listed, but if you have time to add a show I would say An American In Paris is also very enjoyable.
Surprisingly, I enjoyed Neverland. It's has flaws, but I don't regret seeing it. However, I think An American In Paris is far superior. Just my 2 cents worth.
I have seen all of the shows on your list, except the King and I. I would strongly recommend Something Rotten. I think it has a good score as well as a very funny script. I enjoyed it so much, I bought a ticket the next day for my return trip this summer. I would advise against The Visit. I was extremely disappointed. It was the least enjoyable show of the 13 I saw last month. I couldn't wait for it to end. I love Chita Rivera, but I wish I could have gotten the time back and gone to almost a...