If the forecast is looking grim, why not spend your day at Museum of Kyoto? You'll be fascinated by just how much you can discover about days gone by here.
You'll have no end of sightseeing choices when visiting Central Kyoto. Museum of Kyoto is a great place to begin here, but there are lots of other worthwhile attractions to explore. Kiyomizu Temple, Nijō Castle, and Kyoto Imperial Palace are near the collection of historical artifacts and will fill in your day nicely.