Where can I go hiking with my dog? - I am going to punt on this as I don't own a dog and refer you to one book, Best Hikes With Dogs: New York City & Beyond by Tammy L. McCarley, and to the answer to the next question (below). Please note that there are indeed areas in the NYC where hiking with dogs is permitted. Some require the use of a leash and some don't.  Some regulations also vary according to the time of the year with more permissive policies during the off-season than during the peak season.

Are there group hikes for dogs (and their owners)? - Yes.  The Appalachian Mountain Club occasionally has "dog friendly" hikes.  There are also other groups in the NYC area which also organize dog friendly hikes (since I have no firsthand knowledge of these groups so I am hesitant to recommend them but they are easily found). It is considered inappropriate to bring a dog on an organized group hike that is not explicitly labeled as dog friendly without the permission of the hike leaders.

What would be a good hike for those with children? - Another question I am going to punt on since I have limited experience here.  Most of the hikes on this website would be too difficult for little children.  Here are two books that seem to cover exactly this topic, Best Hikes With Children in the Catskills and Hudson River Valley Second Edition by Cynthia & Thomas Lewis and Best Hikes with Children in New Jersey Second Edition by Arline Zatz.

Can you recommend any magazines about hiking? - I highly recommend Backpacker magazine even if you never intend to go backpacking (that is, sleeping outside in the course of a multi-day hike).

Where can I buy hiking / trail maps? - The maps that virtually all hikers in the Greater New York City area use are published by the non-profit New York - New Jersey Trail Conference. They are excellent and will last years as they are printed on an indestructible (Tyvek-like) material or at least until they are superseded by a newer updated version. They can be bought online directly from the Trail Conference.  In addition, many outdoor gear oriented stores such as Campmor, EMS (Eastern Mountain Sports), Tent & Trails, and Paragon carry them.

Which hike is closest to New York City? - The closest two hikes to NYC are the two in Palisades Interstate Park, Palisades Interstate Park: Southern Section and Palisades Interstate Park: Northern Section.  The further one is about 16 miles from Manhattan.