Not really, unless you consider a bicycle a “beast” of sorts. When I was here in May, it was too darn hot to go on any bike tour, morning, afternoon or night. But I think October, now, is going to work out. Here is what I am going to do. First, take a bike tour and get the “lay of the land” for two wheels. With the plethora of cobbled streets, I plan to be extra careful, ride slowly, and try to stop as often as possible.
Here is my general itinerary. You will see many famous places along the way.

Like most tours, everything starts at the Acropolis Museum. In fact, I spent most of my time last May in the shadows of the Acropolis Museum, my hotel was less than a block away. And it might have been the coolest (both as a museum and in temperature) in the city.
Herod Atticus Odeon, a beautiful Roman amphitheater
Pnyx (I wonder how they pronounce this?)
National Observatory of Athens
Thiseio, a scenic local neighborhood
Keremeikos Cemetery
Ancient Agora of Athens, the birthplace of democracy
Roman Agora
Tower of the Winds
Metropolitan Cathedral of Athens, one of the biggest Orthodox churches in Athens
Adrianou Street, the main market street in Plaka
Plaka, the old town (where I like to stay and dine)
Hadrian’s Library (I forgot my library card)
Philopappou
Fethiye Mosque
The Acropolis, the most important archealogical site in Greece
Parthenon, the most important ancient Greek temple
National Garden
Presidential Mansion
Panathenaic Stadium, hosted the first Olympics
Zappeion Conference Center, one of the most beautiful neoclassical building in Greece
Temple of Olympian Zeus
Arch of Hadrian (Pili tou Adrianou), the most photographed monument in Athens

There is a maximum of twelve cyclists. It is a three hour tour (sounds like Gilligan’s Island?) I get a helmet, and pick up and drop off at my hotel!!