A few years ago I rode my bike everywhere and I did hundreds of miles. Let me tell you, there is no tourism like going with the bicycle because you're really close to everything and you can stop whenever you feel like it. Guess what, it's super cheap and you get healthier doing it. Have you tried it?
I agree with you. There are cities that can offer bike rentals and there are some travel agencies offering bike tours. In Japan, you can rent bikes from several coin operated bike rental stations spread throughout the city and return the bike on specified stations when you're done using it. Biking tours are cheaper and allow you to explore other attractions including those unreachable by car or van.
You definitely get a lot more chance to stop and look around on a bicycle. Some places even have multiday tours for cycling. In my area there is a ride called the Kettle Valley Railway that can be done in parts or in its entirety which could take up to 2 weeks. Staying at campgrounds and B&Bs is the way to do this one. Another takes cyclists on winery tours - though I know not how well riding would go afterwards. A third day trip is a tour of local farms once a year known as the slow food ride. There are many tourism options available to the cyclist. Some are in your local town and others further afield. It all depends on your energy level.
Bicycle tourism in itself is an adventure in Greece, because of the tough terrain and nice climate. So the best option in my opinion is to use your bicycle, use Greece as a starting or ending point of your venture and go on a European trip.
In Lisbon I have the same problem, it's called the city of the seven hills, so guess what, we have loads of them. But when riding the bicycle I used to go outside the city and enjoy new places, I used to carry my tent and I can tell you it's an unforgettable experience, even when it rains lol.
