Was there a real city on which the movie Nightmare on Elm Street was based?

Yes. The movie was based on many of Craven's childhood memories, all of which happened in Los Angeles, CA. The initial concept was loosely based on actual cases of refugees from Laos, Cambodia and Vietnam having a series of terrifying nightmares and then dying in their sleep shortly thereafter.

Freddie Kruger was originally intended to be a child molester, but a spate of molestation cases had occurred during production and he didn't want to be accused of exploiting the cases. The character's name was the name of a boy who had bullied Craven in Elementary School.

The decision to set the movie in a small town in Ohio, and on Elm Street, was made so that it had a broader appeal to rural Americans.

My answer is from unofficial sources and articles both fiction and nonfiction from what was said and not said. I am aware of the official answer given by Wes Craven but this is not that answer.

The fictional address of the house that appears in the film is 1428 Elm Street; the actual house is a private home located in Los Angeles on 1428 North Genesee Avenue."

I googled mapped street viewed it and added the picture below with the link to see the whole street.

Google's maps are slightly off but you can see the address on the door frame.

https://www.google.com/maps/place/1428+N+Genesee+Ave,+Los+Angeles,+CA+90046

Now in the movie it appears to be in the city of Springwood, Ohio from the newspapers from the movies.

There is no actual place in Ohio to come close to the city name Springwood in the movie.

Although, I did find this place called Helltown along a road called Riverview, previously Boston Township founded in 1775 is one of the nine townships of the Summit County, Ohio, United States, about 23 miles south of Cleveland.

The city slogan is a very similar match to the welcome sign in the movie. The city was shut down from all the Satanic worship and unsolved missing children from the 60s in that area and as rituals go ritual probably go back to 1775.

In 1974, President Ford signed a legislation that allowed the National Parks Service to buy the area and turn it into a national park. There was no real park ever made nor did it have any real unique features and never really became a park.

No spills or hardship and some of the houses where unusually extravagant for the area to be shut down the way it was. Maybe the majority of the people was just evil and as an extra measure they closed the land. I could not find any official reason why that location was chosen for a park.

The Army was called in to remove the people in that area.

Video of locales being ran out of their homes.

Remember the scene on the movie with the school bus.....the rusting bus in the picture(photoshoped) below was said in that area of a killing spree where at least a dozen children were hacked to death on a school bus. Don't fall asleep and miss your stop.

The sign above is the actual welcome sign but the picture was photoshoped. Notice the slogan for the movie compared to the one in Helltown.

One, two, they are coming for you Three, four, better lock your door Five, six, grab your crucifix Seven, eight, gonna stay up late Nine, ten, never sleep again

Children went missing at night while they were sleeping and taken to this church next to the bus where Rituals were done to them in the basement. I included another picture of the church before the city was shut down.

More Helltown, Ohio pictures:

Houses that was abandoned in the 90s look similar to the Elm Street in the movie.

The jail was the last part of the city to close in the 90s about 30 years after the city was closed. I could only imagine that the perpetrators were kept there until death.

Graves of children around an Elm tree. The Old Boston Township High School

Notice the upside down crosses. Blueprints for this church was used across the US.

Photos of actual missing children from this town looks similar to the movie newspaper.

From the movie.

This would make a good bases for this horror movie. Exact detail are unconfirmed, but you can Google Helltown, Ohio and decide for yourselves.