cipher - Number 1 Mission

When Inspector Kit was just a little kitty, she desperately wanted to be a spy - jetting off to foreign countries, thwarting international diamond thieves.

And now the big day has arrived - her very first mission. And it's rather disappointing. This was not she had in mind - a grubby room somewhere in America.

The room's seen better days for sure - there's not even a stunning view to compensate. The first window shows a brick wall, the second a dead-end street and the third a bit of sky with the top of a billboard.

As for lasers, codebooks and electronic forcefields, forget it. There's a very old map of America and a flipchart with an impressive obscene doodle on it.

In the corner, there's a dusty bookcase with a few old books falling to bits - no-one has touched them for years.

The extremely promising selection is The Life History of the Louse (with pictures-1974 edition), Chart-Topping Hits (1977 edition), How To Keep Your Hamster Happy (1976 edition), Fun and Easy Codes for Kids (mouldy cover only).
Joining them on the shelf are a few rusty staples, some bits of old string and half a dozen drawing pins.

And the mission instructions on a piece of paper torn from the flipchart.

NUMBER 1 MISSION.
Find the state that the bomb has been planted in - X marks the spot.

60659-11160-81874-41475

That's all there is. Apart from a coffee stain. And another obscene doodle.

This spying lark isn't so glamorous as it seems. But the problem has to be solved...

Answer

Send the bomb squad to ...

Illinois!

---

Following the clues . . .

• 
  

  The Windows

  
  
  

  
  

  The first two windows are unimportant. The third window shows the top of a billboard.

  
  

  
  


• 
  

  The Bookcase

  
  

  
  

  The only thing on it that matters is Chart-Topping Hits (1977 edition).

  
  

  
  

These taken together suggest

looking at the Billboard Chart-Topping Hits for certain years, as noticed and pointed out by @incognico whose discovery gave me the fresh insight needed to solve this.
So, what years do we look at? ...

• 
  

  The Mission Instructions

  
  

  
  
  

  The numbers, 60659-11160-81874-41475, now that we know what to look for, look like not just years, but specific dates. So let's find the top singles for those dates:

  60659 is 6/6/1959; the Billboard #1 Single on that date was "The Battle of New Orleans"
  11160 is 1/11/1960¹; the Billboard #1 Single on that date was "El Paso"
  81874 is 8/18/1974; the Billboard #1 Single on that date was "The Night Chicago Died"
  41475 is 4/14/1975; the Billboard #1 Single on that date was "Philadelpha Freedom"

  
  

  
  


• 
  

  The Map

  
  

  
  

  The key here is the line from the Mission Instructions:
  
  "Find the state that the bomb has been planted in - X marks the spot."

  As I suggested in earlier incarnations of my answer, we need to find a way to draw two lines that cross in an X on the map; this requires four locations. Looking up the Billboard hits and noting they all name cities, we now have four locations.

  Drawing lines between New Orleans and Chicago, and El Paso and Philadelphia, gives us:

  

  
  

  
  

Putting It All Together

It's hard to tell on that map where they cross, but it appears the intersection is in Illinois (I redrew straighter lines and the intersection is a bit inside IL, near the Shawnee National Forest). I had Kentucky here earlier, as it's pretty close to the IL/KY border. (And on Google Maps it seems to be inside Tennessee; go figure.)

I'm going with Illinois.

$ $

_{¹ 11160 could also have been 11/1/1960, but no city is named in the song for that date.}