Sorry don't know much about New Jersey.
But we took our toddler to New York this summer and had a brilliant two weeks.
Here is the website I used when we went to NY this August:
https://m.airbnb.co.uk/s/New-York--NY
We found it easier to stay in an apartment than a hotel, as that way we had seperate bedrooms, every local restaurant delivers food, so we could have date nights in the apartment on the nights we didn't have a babysitter (we have a lot of friends and family in NY).
You can enter in the exact neighbourhood in NY that you want to stay in (or just do a more general Manhattan search) plus search by how many bedrooms you need the apartment to have. It's a great way to get a cost effective place to stay, just book a place that has reviews (a bit like Trip Advisor) so you can see what other people thought of it.
We stayed in Upper West Side, partly as it's my old neighbourhood and we would be near friends who babysat, but also as it's a great family neighbourhood. We stayed in an apartment that was one block from Central Park, the Diana Ross Memorial Playground, the Natural History museum and some restaurants we really liked! Also the west 72nd subway is a good one to be near as it's easy to get around the city from.
Other than those there is tons to do in NY with kids:
The Highline is an excellent day out with a little one as it's like one big long exercise run for them, with great views and food trucks along the way!
You can all go and be kids again at FAO Schwartz (and dance on the piano like in Big!)
Depending on how old/ gender of your child - the Plaza hotel does a Eloise themed children's afternoon tea, I'm def doing that with my daughter in a few years!
There are parks and playgrounds dotted all over the city, in the summer most of the playgrounds have water play areas and fountains for the kids to play in so bring their swimsuits or a change of clothes.
I know NY might not be top on everyone's list of where to holiday with a toddler, but I loved going there with our child this summer and we had a brilliant time.
