If you're sitting outside, older children could play on a pedestrian patio (non-restaurant) within your sight line.
They'll accommodate a stroller at a table, but steering to it is tight.
10 Downing St
New York, NY 10014
(at 6th Ave)
They reassured me in advance I could keep the stroller at the table and indeed I could! Not a lot of space, but we made it work and everyone was friendly about it.