In NYC, its really dependent on location. Given Central Park, it is possible to feel like you're away from a city, but it depends on the location. Even in the Summer, if you travel anywhere between the 79 Street Traverse, and North to 110th Street (Park wise), it will be a little emptier than anything below 79th. Anything below the Lake (right near the Bethesda fountain) is horribly overcrowded. More so in the Summer, but you will find crowds even in the fall.
Even though I said location, also if thiers events. Depending on the schedule of events, certain parts of the park can feel very busy (even north of the Kennedy Reservoir).
But the cities huge, and plenty of parks can offer an escape from the concrete jungle. Outer Boroughs more than Manhattan. Bryant Park will not feel like an escape.
In fact, if anybody wants to escape the crowds, its amazing the transition that you will feel being in Jersey City, Hoboken, or even Newark. Even though they are big cities, they often feel empty and provincial compared to the crowds and traffic of Manhattan. Which is the amazing part about this place. You can easily go from an area of 10,000 ppsq-mile to a density of over 130,000 plus. Daytime population is over 4 million on any given workday (Manhattan) and only rising.