From Ginza you are not far from the Arakawa river to the east. Take a look at the route of the HFC Arakawa ride. The route along the right bank (km 15-31) is a nice stretch that can be quite fast if it's not too busy. I really like it.
From Ueno to the river (km 8-15) follows mostly small streets. Depending on your preference, you may want to follow larger arteries instead. I like those quiet back streets, but others prefer a faster pace than possible there.
From the end of the riverside path you can either follow the HFC route for distance and seeing some parks or head back directly towards Tokyo station and Ginza.