Hi Pampam
While I don't have any experience with this, I did find this during a google search:
Renting a bicycle in Greece
Almost every resort town or island in Greece now has at least one shop that will rent you a bicycle (po-THEE-la-toe). Generally, this is a motor scooter rental shop, with bicycles an unloved step-child. Selection and service are limited, especially for adults with long legs. Derailleurs are often badly adjusted and brakes noisy or slack. Many have worse-than-useless rear suspensions that make riding uphill an agony of wasted energy.
Keep in mind that most Greek islands are the pointy end of a submerged mountain. Road engineering is rudimentary. Steep uphills and their inevitable corollary of steep downhills are a fact of life, and don't forget the meltemi and other strong breezes. Working gears and working brakes are vital to your safety and pleasure.
A non-serious cyclist will generally find a rental bicycle in Greece that is better than no bicycle at all, one perfectly adequate for getting to the beach or market. For serious riding to remote, beautiful spots, however, bring your own bicycle or rent in Athens or Thessaloniki from a real cycle shop. Pame Volta in the Athens suburb of Marousi comes well recommended for rentals and self-guided Athens tours. In downtown Athens, Scoutway on Adrianou St. in Plaka offers self-guided bicycle tours as well.
IDEAL is the most common bicycle make in Greece. Their high-end bicycles are adequate. Look for models with Shimano gearshifts and brakes but no rear suspension or fancy gadgets. Rent the tallest bicycle whose top tube you can straddle comfortably. Take a test ride that uses all the gears. Make sure the brakes will hold you on a slope. The shop can probably fix the brakes, if not the gears. Don't forget to have them adjust the seat for full leg extension, and check the tires for full inflation.
Ask for a helmet. Ask for toe clips on the pedals. If enough people ask pointedly, the shop might get some. Take their card with phone number, just in case something goes wrong.
Bicycle theft is rare in Greece, at least outside big cities. Still, the shop should give you a lock and you should use it.
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Rent-a-Bike in Greece: Athens, Crete, Corfu, Mykonos, Rhodes, Santorini. Car rentals in Greece