Kyoto offers so much to see and explore that you have to find the best way of transportation not to hurt your budget. Bicycle is a cheap and convenient way to travel around Kyoto. You can rent bicycles fro shops and some hotels also have bicycle services. Hearton Hotel where we stayed during our trip to Kyoto, offered bicycles for free as long as you make a reservation earlier.
Not to mention that it's environmentally sound and you get exercise, the truth is that there is no better way to see Kyoto than by bicycle. My reasoning is that: 1) the trains don't go everywhere and they don't drop you off close enough to the places you'd want to see, 2) if you use taxis, you'll blow more money than most can afford and you'll be stuck in traffic enough of the time, 3) the buses, are another choice but, you can't just stop anywhere, 4) walking, you'll be exhausted (as we were on our first day).
By bicycle, we were able to cover so much of the city and see so much more of it in less time than it would have taken us any other way.
If you don't have a bicycle with you, you can simply rent them as we did. They're not so expensive only costing about 1,500 yen a day or so and worth paying the insurance for, just in case, the bikes are stolen or damaged. If you have 3 days, and you have a bicycle, you can pretty much cover all of Kyoto from the West to the East and the Northern area down to the South (where Kyoto station is). We rented 2 bikes from Hotel Kyoto Yayoi Kaikan.
Other locations, such as near Kyoto station, are mentioned here:
Bike rental locations in Kyoto
On the downside, we found parking to be difficult in downtown areas like Nanajo Street. And we actually had to pay for parking at Nijo Castle (Nijo Jo).
Kyoto is best traveled by bike. It's an enormous city and the public transport is so that you have to change a lot to get to your destination.
The roads are somewhat steep in north-direction. But after visiting the temples in the north, it's nice to relax on your bike southwards.
Keep in mind that they drive on the left side of the road.
The best way to get around and to see Kyoto is by bicycle. You can hire a bike by the day from various places dotted around the city, and cycling in Kyoto is very safe because everyone cycles on the pavements! Also, because Kyoto itself is a very safe city, there's no worries about your bike getting stolen! (I even saw people who trustingly left their bicycles on the side of the pavements without chaining them up - it must be that safe!)
There ARE Trains, busses and cars but, if you are healthy and relatively active, I suggest taking out your Mama Chrry Bicycle.
EVERYBODY has one!! You can rent one or just buy one for as little as 3000yen.
Kyoto is mostly flat and taking a bicycle is not only cheaper but is faster than most other forms of travel (even, maybe, than a scooter) because there are no road rules for cyclists to follow and you can even go up on the sidewalk.
Be careful to lock up you bicycle thou. The one thing NOT safe is an unlocked bicycle in Japan!
And eatch where you park it. The government also tows.
Bicycle is very popular and useful way to see this city if you want to avoid traffic or crowded buses. Kyoto is mostly flat which shouldn't be much of a problem to explore the city this way.