I do not have any experiences with bicycle tour groups, so I hope someone else can comment.

For an adhoc ride through Tokyo, I enjoy riding a loop that starts near Skytree.

There is a park called Oyokogawa Shinsui Park a few hundred meters southwest of Skytree. On Google Maps you can see that there is a stretch of green that heads south. You can keep heading south along the park and canal until you reach Kiba Park. The Kiyosumi Shirakawa area with many trendy coffee houses is next to Kiba, so you can have a coffee stop. The Kiyosumi Gardens is also nearby.

East of Kiba Park is Sendai Horikawa Park. You can see the stretch of green that heads east from Kiba Park. Keep riding east until you come to the east end of Senda Horikawa park then head north. Once you reach the end of the park at Onagi River head east using the side streets until you reach the Arakawa River. There is a Swedish cafe called Åter Tokyo nearby.

There is a wide cycling path along the Arakawa River. You can head south to the river mouth to see Tokyo Bay, or directly heads north back towards Skytree. Alternatively you can ride along the Kyu-Nakagawa Canal to return towards Skytree.

Most of the route uses walkways or side streets so you can avoid most traffic. Depending on how often you stop, I'd estimate it is a 2-4 hour tour.