Take Toda Bashi Bridge, which is near JR Saikyo Line, then head south along R17. R17 is not bad for biking.
Take Hakusan dori avenue at the junction near Sengoku Station. Hakusan dori is very wide and comfortable for biking.
Then you'll reach at Imperial Palace. Uchibori dori avenue, which is a loop road of Imperial Palace, is also comfortable. Tokyo Tower is right over there.
As for the Arakawa, the right bank is good between Toda Bashi and Hanekura Bashi (R463, Sakura-ku, Saitama-shi). The north of Hanekurabashi, there is a cycling road.