K-R Meritt

It was the hot dog vender on Fifth Avenue that put me on to it: "I don't sell coffee, but there's a coffee counter just under the stairs down there," meaning the ground floor entrance of the Arsenal building, tucked into the east edge of the Central Park Zoo and now housing park permits and related offices. NYC employees are the greatest civil servants in the world, and none more friendly or helpful than those who work for the Parks Department. The snack bar menu is limited, but the prices are employee cafeteria affordable, keeping workers from having to go off-premises and not having to calculate UES rent into the cost mix.
Restrooms are clean. Elevators work. Wheelchairs move through freely.
But the best feature is the 3rd floor lobby, equipped with tables, folding chairs, and pigeon-free indoor versions of park benches, where you can eat your lunch, work the NYT crossword, or check out the exhibition on display, currently showing memorials and monuments of WW I in Central Park. There is no particular accommodation for children, but the vibe is relaxed: "It surely wouldn't hurt to linger a few more minutes..."
One wouldn't come from Des Moines just to visit the Arsenal, but if you find yourself as near as Hunter College during office hours, you might want to keep it in mind. On the way out, stop on 1st or 2nd floor to glance at the whimsical history in the lobby murals.