First, I definitely think it is not cool for people to not offer seats to pregnant women, those with babies, the elderly, etc. I always look to offer my seat and actually will just stand even if there are a few open seats just so I don't take the last one. To be that is an obvious one (that said, I try not to judge people that don't get up as you never know what physical limitations they may have that aren't apparent)
To me the dicier situation is a man offering up his seat to a perfectly able woman. I actually did that once at work and got "reprimanded" as that could be considered sexual harassment for insinuating a woman needs a seat more than a man. oh well.
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OK, now chiming in with some thoughts on your NYC trip:
- Totally hear you about wanting to minimize number of bags with having all the baby stuff too. I think as long as you have one carry-on bag (be it Dug's backpack or whatever) that you can at least fit some clean underwear in for an emergency if your bags get lost, you should be ok
-As far as strollers in the restaurants in NYC, most are pretty well equipped to handle it. Depending on how much room they have they may keep it up front or ask you to fold it up, etc. Basically, they will make it work, you just might need to be a little flexible as to what they do with it.
- As far as the diaper bag, as long as you feel you will be able to carry what you need in the changing kit, etc. they I think leaving a giant diaper bag at home makes sense. We have a few sized "diaper" page (the smallest of which sounds similar to your changing kit) and do use that quite often. You could also bring both with you (use the diaper bag as your carry on and pack the changing kit) and then see how things go with just using the changing kit for outings, but at least you have the larger bag in case you find you need it
- Did you look into pre-arranging a town car or do you have a place you know you can just call for one? I've never done that (either had one pre-arranged or just used cabs)
- Definitely see if you have time to walk around the seaport area - assuming the weather is nice it is a very nice place to take in the views, etc.
- The plans for your first day sound good. I always allow a little extra time to walk places - just if you get off the wrong direction or get caught by lights etc. Also, I am awful with directions in the city (just get turned around a lot) so I find I use google maps on my phone to help out a bit
- I don't know that area very well as far as places to eat. There are a number of options near the seaport - I know there is a sushi place called SUteiSHI (I believe I recall you mentioning Dug liked sushi). There are also a lot of places near Wall St. but they are mostly either corporate/business type places or fast food/bars not a lot of family places
- Another option to eat that is closer to the Ground Zero Memorial is Brasserie Les Halles. It's one of the places owned by Anthony Bourdain and actually fairly low key/not super expensive
- There are lots of nice playgrounds in the city. I don't know the Pearl St. one specifically but definitely check it out.
- As far as taking the FDR, you should be ok as long as you are before rush hour (I'd say before 4pm you should be fine). It still might get backed up and seem crowded, but despite that it will still be your best bet vs. just taking avenues with lights or cutting all the way over to the West Side Highway
- There are some nice areas of Kingston and some good restaurants there too if you want to stop. Also, on the other side of the river from Kingston is Rhineback which is a really cool town with tons of great restaurants and very walkable
- Glad Izzy enjoys the peapod. I mentioned that to my wife that you were considering that and she said she knows a number of people who have used that with success ... let me know how it goes!
- Depending on what side of the river you come down there will be a number of places you can stop at for lunch ... heck you could stop at our house since you will (potentially) go right by
- High Line Park is very cool - and I think you will be pretty close to the northern end of it. If the weather is nice might be worth it. There are a lot of street vendor type places on it, though I think they are further south
- Another option is just walk a couple of blocks north to Bryant Park which is on the back side of the NY Public library
- Your plans sound great - though sounds like a lot (though maybe b/c we live so close we never plan "that" much to do in one day). Also, most of the museums have cafeterias that are usually pretty nice so you can also do that.
- If you go to Rockefeller center, if you are into this, there is a really good wine bar there called Morrell Wine Bar & Cafe
- Does seem like you have a lot of walking (and don't forget that there will be a lot of walking at your destinations - museums, etc.) so if you get tired plan on some public transportaiton. Cabs can work and Subways are efficient (especially when you don't need to deal with a stroller)
- There are a lot of places to eat near where you are staying - you can just ask the front desk or concierge for recomendations. You can also just google search for family friendly restaurants in the areas you will be at.
The thing that bothers me the most, though, is that boarding the bus these same people were so rude - we were literally the first people at the bus stop (remember - we saw the previous bus pull away) - but everyone was shoving in to board in front of us and I felt powerless to cut my way back in front of them because I was holding Izzy and trying to keep Dug and the stroller close behind me. I was getting cut off left and right by people who had arrived after us and would go on to take "our" seats. 
So, hoping it will be okay during these two nights.
I only know how to install with LATCH and it was required in all vehicles since like 2003 or so. I can't imagine this van was that old, but there was nothing. However, the driver was familiar and he was able to help quickly secure the seat with a seat belt. Got Izzy in and we got going:
