Thoughts on your NYC Itinerary:
Day 4 - Free Tours By Foot (NY in one day at 10am to 4pm) Tour covers the Wall Street, Financial District, New York Stock Exchange, Trinity Church, World Trade Center, 911 Memorial, Woolworth Building, Greenwich Village ,Washington Square Park, SoHo’s Cast Iron District, Little Italy, Chinatown, Chelsea Market, The High Line Park, and much more.
I'm with you in that I love walking tours, and Free Tours by Foot is a fave. I think, however, that most of the stuff on this particular tour is not actually that cool or fun, and it sounds like a long day (NYC gets really, really hot if you're coming in Summer, and if this were me I would get very cranky). Wall St/FiDi/Stock Exchange has a bit of "old New York" feel in certain spots, but is mostly charmless, WTC/9-11 Memorial you're already seeing (the museum, I've heard, is excellent), Woolworth Building is nothing, Cast Iron District is a made up thing for tourists, Chelsea Market is cool but not where you want to be with a big group, ditto the High Line.
I recommend you do about half the stuff that's on this tour, and do it independently in your own time. I know it's tempting to want to see as much of the city as possible, and a whole-city tour seems like the answer, but I think doing fewer things more slowly will be more enjoyable and will give you a better sense of the city. Moreover, you simply cannot see all of NYC even in a lifetime, so release yourself from that obligation. Here are my recommendations:
The High Line, Chelsea Market, and Washington Square Park are all 100% navigable on your own, in your own time. You don't need more than an hour for each, unless you're planning to do serious shopping at Chelsea Market. When you go to Washington Square Park, you can wander in any direction and find cute coffeeshops, bars and restaurants, which will satisfy your "Village" checkbox. Little Italy and China Town are all about food - I recommend Wo Hop in Chinatown and Paesano's in Little Italy for sit-down meals.
When you go to the Statue of Liberty, you can pop over to Trinity Church or the Stock Exchange on your way to/from the Ferry - if, that is, you feel strongly about it, which you don't need to. If you don't feel strongly, skip it. If you're doing this, I also recommend a stop in the new WTC PATH station - sort of a futuristic Grand Central.
And, speaking of the Statue of Liberty, it definitely does not require an entire day. I've personally never been to Liberty Island (where the statue is), but the ferry there is only 15-20 minutes and you're not going to spend more than an hour or two at the statue if you're going in the pedestal. You might even find that a quick round trip on the Staten Island Ferry (free, 20min each way) gets you better views of the statue or that a trip to Ellis Island gets you both great statue views and also a cool museum experience.
I also recommend you spend a bit of time in Prospect Park, and/or in Brooklyn Bridge Park (and if you do, eat the best pizza at Juliana's nearby). I also notice that your NYC itinerary includes no museums, and I feel compelled to press you to change that (the Brooklyn Museum is near where you're staying, incredible, a manageable size, and pay-what-you-wish, and also did I say incredible?)
Also, for this itinerary, you should absolutely get the weekly metro card. :)