If the forecast is looking bleak, why not spend the day at Teikoku Databank Historical Museum? You'll be surprised just how many interesting facts you can uncover about days gone by here.
Located in Shinjuku, this collection of historical artifacts is well worth a visit. But you'll find plenty more to see in this area. Tokyo Skytree, Tokyo Tower, and Tokyo Imperial Palace aren't too far away from Teikoku Databank Historical Museum.