Every Sunday, the car traffic is prohibited on the road before the Imperial Palace.
From 10:00am to 3:00pm, the road is opened only for cyclist.
"The Palace Cycling Course", operated by Japan Bicycle Promotion Institute(JBPI) is just only 1.5km course along east side of the Palace, but unique because it is rare to find such event - shutting out cars, and open the road for cyclist every week - in Japan.
Even if you don't have bike, you can rent one for free. They have a variety of bikes including MTB, Road, City Bike, Kid's bike, and Tandem.
But keep in mind that you can't leave the Palace Cycling Course with the rental bike.
Please refer to the following link for more information.
http://www.jbpi.or.jp/english/pc1.html
Enjoy the car free road with your family!
maki