NewPing Library: HC-SR04, SRF05, SRF06, DYP-ME007, Parallax PING))) - v1.7

@hbaxton

Take a look at this sketch. I reworked your sketch and put the motor running part into a function then, made it work with blink without delay style. It is untested but, I think it will work.

#include <NewPing.h>
#include <AFMotor.h>


#define TRIGGER_PIN  7  // Arduino pin tied to trigger pin on the ultrasonic sensor.
#define ECHO_PIN     7  // Arduino pin tied to echo pin on the ultrasonic sensor.
#define MAX_DISTANCE 200 // Maximum distance we want to ping for (in centimeters). Maximum sensor distance is rated at 400-500cm.

AF_Stepper motor(200, 1);
NewPing sonar(TRIGGER_PIN, ECHO_PIN, MAX_DISTANCE); // NewPing setup of pins and maximum distance.

unsigned int pingSpeed = 1000;  // How frequently are we going to send out a ping (in milliseconds). 50ms would be 20 times a second.
unsigned long pingTimer;        // Holds the next ping time.
unsigned long motorTimer;       // Holds the place for motor speed adjusts
unsigned int adjustTime = 1000; // how often to adjust the speed of the motor
int rpm =10;

void setup(){
  Serial.begin(115200);
  pingTimer = millis(); // Start now.

  Serial.println("Stepper test!");
  motor.setSpeed(100);  // 100 rpm   
  motor.step(100, FORWARD, SINGLE); 
  Serial.println("step done");
  motor.release();
  delay(1000);
}

void loop(){
  // Notice how there's no delays in this sketch to allow you to do other processing in-line while doing distance pings.
  if (millis() >= pingTimer) // pingSpeed milliseconds since last ping, do another ping.
  {   
    pingTimer = millis() + pingSpeed;      // Set the next ping time.
    sonar.ping_timer(echoCheck); // Send out the ping, calls "echoCheck" function every 24uS where you can check the ping status.
  }

////////////////////////////////////////Here is the new part that will run your motor on a timer
  if (millis() >= motorTimer)
  {
    motorrun();
    motorTimer = millis() + adjustTime;
  }
}

void motorrun()
{ // this is the function that will run your motor when called
  Serial.print("setting RMP = ");
  Serial.println(rpm);
  motor.setSpeed(rpm);
  Serial.println();
  Serial.println();
  motor.step(100, FORWARD, SINGLE);
  rpm = rpm +10;
}


void echoCheck() { // Timer2 interrupt calls this function every 24uS where you can check the ping status.
  // Don't do anything here!
  if (sonar.check_timer()) { // This is how you check to see if the ping was received.
    // Here's where you can add code.
    Serial.print("Ping: ");
    Serial.print(sonar.ping_result / US_ROUNDTRIP_CM); // Ping returned, uS result in ping_result, convert to cm with US_ROUNDTRIP_CM.
    Serial.println("cm");
  }  
}