Found Central Bike Tours on Trip Advisor. Liked their location (virtually beside Central Park), liked their website (they were the only bike company I saw that had a map of Central Park), and liked the fact that I could get a discount by paying online in advance (biketourscentralpark.com).
My family took the 2 Hour VIP Tour of Central Park, which I liked because it was a private tour, and we could take our time with our young children, go at our own pace, and stop to take pictures when we wanted to.
We met our guide Sergio in front of the Argo Tea Cafe at 1792 Broadway, just a block or so away from Columbus Circle.
They had an appropriately-sized bike for my 11 year old, and a tandem for me and my younger daughter. All were newer 7-speed bikes. They didn't provide locks, but anytime we stepped out of sight of our bikes to take pictures, our guide stayed behind to watch the bikes.
This was a great way to see and learn about Central Park, New York City's number 1 tourist attraction, and I imagine the residents #1 thing-to-do also.
Sergio, who has done these tours for decades, was very knowledgeable and had lots of information and stories to tell. He also showed us around for over 2 1/2 hours even though it was a 2 hour tour.
The 843-acre Central Park has been in more movies than any other location in America. We got to see lots of these interesting / famous sites including The Mall, Bethesda Terrace, the Alice in Wonderland Sculpture, the Jackie Kennedy Onassis Reservoir and Shuman Running Track, Belvedere Castle, Turtle Pond, Sheep Meadow, the Bow Bridge, the John Lennon Memorial - Strawberry Fields, and the Dakota.
The bike portion is about 6 miles, but there are a lot of stops, and my children had no problems whatsoever. There are places to stop for drinks or snacks if desired.
One final thought - we had previously taken a 6 1/2 hour walking tour of Manhattan that included Central Park. Nevertheless, we saw lots of new things and heard lots of new stories on the bike tour.
Visited May 2016