Jeremy, as Brent mentioned, there are tons of threads about where to eat on WB.
As for places to stay, I would stay AWAY from Times Square. It’s a tourist trap nightmare, loud, and with no redeeming qualities that I am aware of. I say this as a native New Yorker. If you really must, walk quickly through it, throw up, then go somewhere and take a shower.
You are coming with family, so stay in family-friendly areas and use the subway/buses/taxis to get around. Don’t forget those two flat things at the bottom of your legs: your feet. This is a walking town, so bring good shoes. The best way to experience the city is to walk it. Upper East/West Sides come to mind, as there are tons of cheaper apartments to rent in those areas (all relative of course, this is NYC after all), and you’re right by Central Park and the Hudson Riverpark. There are also good food/wine stores there should you want to stay in and cook. Tribeca is still pretty good, but avoid the Meatpacking District (very drunkenly loud on weekends), and parts of the East Village might be a bit much at night for kids (good for us, however). The Financial District and Battery Park might be tempting but again can be a bit of a hike depending on where you end up.
Things to see are all the museums of course, the Highline Park (do NOT miss this or I will warn Alan that you are going to sneak into his cellar), walking the Brooklyn Bridge (heck apparently anyone can also climb it, but you might want to avoid that), and exploring parts of Brooklyn. Don’t miss the other boroughs like Queens (great Greek food, some awesome Thai) and Staten Island for, of all things, Sri Lankan food. Do the free ferry to Staten Island even if you don’t explore the island, you will literally be looking up the Statue of Liberty’s skirt. Central Park, the Hudson Riverpark, the East Village, the West Village, the Meatpacking District on a weekday, Chelsea Market, Union Square Greenmarket, the list goes on and on. It really depends on what you and the family want to see and have time to do.
BTW, what airport are you landing at? This is important, as we shamefully do not have a direct public transportation system to them. You’ll be stuck taking cabs from JFK/Laguardia, and rail if they fix the train to Newark or shuttle bus.
Lastly, please reach out directly via PM if you want a New Yorker’s views of areas you are thinking of staying in. I’d be happy to help out. And please reach out should you wish to meet up for a Burgundy or three.
Cheers!