What did a young lad from 10 to 17 do for play time in New York City in the fifties?   Come Saturday morning most young lads left their house at about 9am and maybe came home for lunch.
  But mostly they stayed  outside until the street lights came on at dusk. 
What the hell did they do with all that time?  A myriad of possibilities, but let’s talk about just a few. 
First, if Donny had at least one friend, he had many options if he had a pink rubber hi- bounce ball made by Spalding ( we called it a spaldeen). And even more if he had part of his mom’s broomstick.   With just the ball they could play stoop ball or  box ball   Add the broomstick you get stick ball which had many versions. 
Most town home apartments had steps in front.  About  5 steps to the front door. That was called a stoop.  In the summer with no air conditioning, we all sat outside on the stoop until the wee hours cause it was too hot to sleep. 
In the daytime we could play stoop ball. If you threw rhe spaldeen at the stoop from a few yards it would bounce toward the street where your buddy/opponent would be standing  if he caught the ball on the fly or on the ground you were out.  If it went by him, it was a hit. Each time you played you determined what was a single, double etc. if you hit the point of the step with the ball it went a mile ( like across the street). Over your buddy’s head could be a home run.     It was all honor system  No refs or umpires.  It worked and we laughed a  Bunch.
Box ball just used the sidewalk divisions or you could chalk in the boundaries.  You used your hand and the spaldeen and sorta played tennis with no net.  The ball had to bounce once in his box and he had to hit it over the line to your box.  Pretty simple but lots of discussion/ yelling about in or out calls.  But mostly laughing.
If you only had two of you, you could play stick ball. You need a handball wall or stone wall.  You drew a big rectangle on the wall.  Bottom line about knee high.  Top line about shoulder high.  Side lines about 2-3 feet apart ( how big is your broomstick). That was your strike zone.  Your buddy stood near the drawing with broomstick in batting stance.  You threw the spaldeen at the strike zone trying to strike your opponent out.  You called balls and strikes   Honor system.  He tried to hit the ball.  You both determined what constituted a single double etc. Two young lads could kill hours playing stick ball with no adult supervision to foul up your fun.
If you had more than two and up to 10 kids, you could play in the street using a manhole cover as home plate.  Yes, I got my finger stuck in a manhole cover hole once and held up traffic a while. I was playing catcher and thought it was cool to stick my damn finger in the hole. It wasn’t. I heard Willy Mays played stickball as a kid.  He did ok.  But he wasn’t a Yankee enuf for now.  See ya.