The Imperial Palace Bike Ride is a great Sunday activity, especially if you have kids. The city of Tokyo has bikes at hand for you to do an easy 3km, non-elevation course halfway around the Imperial Palace grounds. The streets are closed for motorized traffic, so all the bike junkies (including those who bring their own bikes) can mosey around the 5-lane streets, only occasionally observing the traffic lights for crossing pedestrians.
All you need to do is fill in an application form (easy enough to do with no Japanese language skills – you only need to give your name, address, age and gender) and line up to get your bike. You are then politely asked to only do one round and return the bike, but no one says you can’t just line up for another round. They also offer tandems, which is great fun. The idea is to enable this course for non-cyclists and visually impaired people. There are even free cycle lessons (in Japanese) for those who can’t cycle.
The bike desk is open from 10:00-15:00 on non-rainy Sundays (decided one day prior if the forecast is 50% or more chance of rain) and it can be found next to the Kokyo-mae koban, a 3-minute walk from Exit 2 of Nijubashi Station on the Chiyoda Line, or a 15-minute walk from the Marunouchi side of JR Tokyo Station. Detailed information can be found here. Also check out the Tokyo By Bike article on this topic as well.
The most adorable place in Japan.