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4-5 km walking distance - rough estimate!
At the airport go to Terminal 1, Regionalbahnhof, take the S-Bahn (sign: white S on green background; trains: usually red) S8 or S9 in the direction Offenbach or Hanau; every 15 minutes; on track 1 most of the time
The route of the S8/S9 for your orientation:
  Frankfurt (Main) Flughafen Regionalbahnhof
  Frankfurt (Main) Stadion
  Frankfurt (Main) Niederrad Bahnhof
  Frankfurt (Main) Hauptbahnhof tief
  Frankfurt (Main) Taunusanlage
Exit the S-Bahn after ~14 minutes at "Frankfurt (Main) Taunusanlage".
#1 Viewing platform at the top (185 meters) of "Maintower" "Main" like the river here in Frankfurt. Small entrance fee, security check. Nice views over Frankfurt.
#2 European Central Bank, €-sign in front
#3 Goetheplatz, statue of the famous german writer, born 1749 in Frankfurt
#4 St Paul's Church, an important place in germans democratic history
#5 "Römer" - city hall, important place for tourists :-)
#6 memorial plaque: book burning 1933
#7 Eiserner Steg pedestrian bridge, nice panorama of frankfurt, short walk along the river Main, lots of museums and Schweizer Straße with traditional applewine restaurant on this side of the river
2nd #7 (sorry, my mistake :-)): Cafe Metropol - nice patio, breakfast the whole day, organic/vegetarian/vegan/local food, home-made cakes, try the peppermint iced tea!
#8 Frankfurt Cathedral - tallest building (95 meters) in Frankfurt until 1961 :-)
#9 Fountain of Justice, souvenir shops
#10 "Zeil" - one of the most famous and busiest shopping streets in Germany...
#11 Viewing platform at the top of "Zeilgalerie", use the entrance/elevator to "ASTOR FILM LOUNGE"
#12 old frankfurt stock exchange
#13 unofficial name of this street: Fresgass - "Grazing Street"
#14 Opernplatz; old opera, Fountain
I hope, you will enjoy this tour.
Back at Frankfurt (Main) Taunusanlage S8/S9 in the direction "Wiesbaden Hauptbahnhof" will bring you back to "Frankfurt (Main) Flughafen Regionalbahnhof" in ~13 minutes - every 15 Minutes.
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take S8/S9 (s-bahn, follow the green "S" signs or ask for S-bahn)
then you have different options: 
get out at "hauptwache" that would be the old part of town, and wander around there.
But another guy recommended a short walk, along the european central bank as well: 
Hauptausgang Hbf, Münchner Straße (wenn ihn das Rotlichtviertel nicht irritiert), Willy-Brandt-Platz (EZB), weiter zur Hauptwache, runter zum Römer, Dom über die U-Bahn zurück (oder evtl. fährt der ebbelwoi-Express)
wenn Zeit ist, kann man von da aus auch noch zum Main runter
oder von Hauptwache aus mit der U-Bahn zum Willy-Brandt-Platz, EZB und dann die Route
Translation: 
Main exit Hauptbahnhof (main station), take Münchner Strasse (if the red light district wont irritate you), go Willy-Brandt-Platz (there is the Eurpean Central Bank, EZB), go on to Hauptwache, go down along Römer and Dom (big church) and then take the U-Bahn to get back (or maybe you can take the ebbelwoi-Express). 
If time, you can go to the Main (river) as well.
Another Option would be from Hauptwache with U-Bahn to Willy-Brandt-Platz and then following the route above.
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Alternative proposal I wrote in the past for someone else:
https://kuix.de/blog/index.php?entry=Exploring-Frankfurt/Main-during-a-FRA-airport-stopover