Fun Home is truly outstanding, one of the finest shows I have ever seen, extemely inventive, cast outstanding- I totally recommend. I have not yet seen the revival of King & I, but friends who have seen it absolutely loved it. I am a big Kelli O’Hara fan, Ken Watanabe is already gone for another commitment.
I can also recommend Gentleman’s Guide to Love and Murder, last year’s Tony winner. I had no interest in seeing it actually but went with my cousin and her friends who came to NY for a theater weekend and really enjoyed it -very entertaining and clever. Jefferson Mays is a delight. Sadly Bryce Pinkham left to star in The Heidi Chronicles which was unfortunately short-lived. (I saw that and thought it was good, as a revival, it did not find an audience).
Matilda is very charming. The choreography with the children is well-done as is how they relate Miss Honey’s back story.
If I could go to NYC right now and see any show, I would try to see Hamilton, Fun Home or Beautiful. My daughter is lucky in that she has seen all three.
If you want funny, see Something Rotten
If you want emotionally intense, see Fun Home
If you want edgy (and can get tickets) see Hamilton
Based on the shows you listed as having seen in your OP, I would recommend Something Rotten
President Obama saw Hamilton this afternoon. I don’t think he had a problem getting a ticket. 
He’s coming back, I believe in September.
I’ve heard fabulous things about American in Paris as well - the book was totally rewritten, the choreography is amazing, and of course, the Gershwin score is second to none.
"President Obama saw Hamilton this afternoon. I don’t think he had a problem getting a ticket>’
He took his daughters. Cast was thrilled he was there.
http://news.yahoo.com/president-obama-girls-catch-hamilton-broadway-191715589–politics.html
Kinky Boots was a lot of fun.
I have heard great things about A Gentleman’s Guide to Love & Murder from a number of friends.
I tried to get Hamilton tickets for September and the site says that the earliest available are in November.
Rather than suggest any one play or musical, I thought I’d give you a tip. We always try to buy half-off tickets at the TKTS booth on Times Square, which opens at 3 p.m. There is always a mob of people and long wait, and when you get to the window they don’t give you very much time to think.
A couple of years ago I decided to take the subway to Brooklyn and use the TKTS booth there. It opens at 11 a.m. There was only one other person in line, so I let them go in front of my while I considered the best offereings that the guy had. I ended up paying half price for front row tickets to Phantom. Yes, the show is old and I had seen it a couple of times, but it’s really neat to sit on the front row. And it was the first time my kids had seen it. So I would strongly recommend the Brooklyn TKTS booth which opens at 11 a.m.
Also, going to try to buy tickets at 3 or 4 is a pain. Then you have to go back to your hotel and change and rush to the theatre, or else you have several hours to kill. Having the tickets in hand before noon is a real bonus.
To piggy back on @EarlVanDorn 's post - there is an app for TKTS that will show you what shows are available that day at both the Times Square and Southeast Seaport booths. That way you can decide what you want while you’re standing in line, and put shows in priority (“If they don’t have A when we get there, or the seats are lousy, we’ll take B. Or maybe even get down to C.”)
Family members loved An American in Paris.
Another vote for the South Street Seaport TKTS–never had a line there. But I don’t think they offer same day tix for matinees. It’s bit of a hike to get there, but I’d rather be riding on the subway and walking than standing forever in the Times Square TKTS line. Pet peeve: TKTS customers who haven’t a clue what they want til they get to the counter and then argue over what show to see and what seats are acceptable. I’ve often wished the clerks would take the approach of the Soup Nazi and banish the laggards!
I loved Beautiful, but it’s best for Carole King fans. Something Rotten was cute and entertaining, with a lot of dancing, which pleased me, but it’s not the kind of show that stays with you. The King & I is a huge treat for those who appreciate old-school musicals, and I don’t think not having Ken Watanabe anymore is a huge loss–but I would be sure to see it with Kelli O’Hara, who is currently on vacation. I didn’t see Fun Home, but D loved it; she tends to prefer the more downbeat stuff, like Spring Awakening and Next to Normal, though I don’t know if that’s a fair characterization of Fun Home.
We saw On the Town this past month. Loved the show - a lot of dancing involved too, which made D happy. Saw A Gentleman’s guide to Love and Murder earlier this year - a real fun show and Jefferson Mays was a hoot. I’ve heard great things about Hamilton - maybe on our next trip.
Just saw Kinky Boots and it was wonderful with great songs, costumes and story. The lead was amazing!! Everyone in the theater was smiling and enjoying it.
Several friends who have seen Beautiful thought it was great too.
We enjoyed Something Rotten, but it’s not a classic.
Another tip about the Times Square TKTS–there is a separate, much shorter line for plays (as opposed to musicals). So if your top choice is a non-musical, ask the guards where the “play line” is.
Just heard Rumer Willis will star in Chicago this fall. Might be fun to see …
I know it didn’t get great reviews in NY, but I’d go see Larry David’s Fish in the Dark. I usually like everything he does–loved Curb Your Enthusiasm.
Saw Fun Home – small theatre, intimate, beautiful music, moving. I also saw Kinky Boots – big, loud, flashy, funny. Enjoyed both, although they were quite different experiences. If you want to see Fun Home, you should buy tix in advance. Small theatre, popular show, could sell out on your desired dates.
Recently saw The Book of Mormon. Loved it. Even the usually laconic DH was effusive in his assessment. But at almost $600 for 3 people, won’t be doing any more shows in the near future 