The bike ride along this corridor would partly be on a street; but you certainly couldn't call it a busy street.
The in-park portion starts in Kissena Park, at the corner of Kissena Boulevard and Rose Avenue. You take that path east. When it crosses 164th Street, it becomes a regular street, Underhill Avenue. But it is a very quiet street with houses only on the north side (to your left). On the south side of the street is the park.
You take Underhill a few blocks to where it dead-ends at 170th Street, and you go right to resume the in-park portion of the path. Take this, still going east, to where it ends at Utopia Parkway.
You will then have to turn left to go north for a half a block to get back to Underhill Avenue. The
official New York City bike map says that you can use the west sidewalk of Utopia Parkway for this.
Then you will turn right at Underhill Avenue, and cross Utopia Parkway with the light. When you have crossed Utopia, you will find that Underhill has a painted green bike lane going east. This lane is flush with the curb; there is no parking on that side of the Underhill. And, here again, there are houses only on the other side of the street (the north side); the south side (the side that you'll be on) abuts the park.
Take Underhill all the way to just before it hits the L.I.E. service road; I believe the street there is 196th Street. There you will see on your right an entry back into the park, and a path that leads you onto a bridge over the L.I.E. From this point on, you are only on in-park paths.
This path continues, almost touching Francis Lewis Boulevard behind a high school, and then turning south to parallel Franny Lew. It is now the Vanderbilt Motor Parkway. Continue south on it, and it eventually turns left (east) and goes over Francis Lewis Boulevard.
It continues east until it ends at Alley Pond Park.
That trip is about five miles.
Here is a map of the route:
https://drive.google.com/open?id=1SR...es&usp=sharing