There are 10 Valuable Object Locations in Assassin’s Creed Shadows. The valuable objects are collectibles needed for side quest Valuable Reflections. This page shows the Valuable Object Locations.
Valuable Objects are found inside military locations, mostly inside 
Castles. When you go near them they get marked by a white 
icon on the map. They only show on the map when fully zooming in. You can also filter for them on the map by pressing Dpad down.
All of them are still obtainable after the story in free-roam, nothing is missable.
Izumi Settsu
Valuable Object #1: Insect Cage – Sub-Region: Katano
Valuable Object #2: Sake Flask – Sub-Region: Amagasaki
Yamashiro
Valuable Object #3: Umbrella – Sub-Region: Yamazaki
Omi
Valuable Object #4: Clockwork – Sub-Region: Ado River Valley
Yamato
Valuable Object #5: Calligraphy Set – Sub-Region: Nara Heartland
Kii
Valuable Object #6: Ammo Box – Sub-Region: Saika
Valuable Object #7: Flower Vase – Sub-Region: Nakahechi Route (inside “Sandanbeki Cave” enemy outpost, entrance shown in 2nd image below, use L2/LT to see a white dot inside the camp that marks it)
Tamba
Valuable Object #8: Chinese Lacquered Furniture – Sub-Region: Kameyama
Valuable Object #9: Fan – Sub-Region: Miyazu Bay
Wakasa
Valuable Object #10: Kimono – Sub-Region: Lake Suigetsu
For all other collectibles check out the Assassin’s Creed Shadows Collectible Guide.
Shazam_Savage says
If we found a valuable collectable prior to finding this quest, and sold it at a vendor, would the item still count for the quest line?