Okay, after a bit of running around, here's what I found:
Tier 9
Arirang
Tier 6
Pacific
Tier 5
Asuka, Atlantic, Catskills, Chesapeake, and Formosa
Tier 4
Europa, Great Lakes, Lake Superior, Mizuho
Tier 3
Balhae, Hokuto, Legends, Napa Valley, Sakura, Sonoma
Tier 2
Baja, Izumo, Yamato
Tier 1
Drachenfels, Lake Austin, Oceania, Siege Perilous, Wakoku
Tier 0
Mugen, Origin
Note: On all shards except Siege, I only checked the museum in Trammel. I figured that since Vesper is a faction town, the guard zone's been gone for many months and it's doubtful many people would continuing donating at the museum in Fel.
These are the exhibits that show up for each of the tiers:
Tier 0: No exhibits.
Tier 1: The Necromantic Arts. In the display case: grave dust, nox crystal, wyrm's heart; necro spellbook; animate dead, horrific beast, and vampiric embrace scrolls. Dark south-facing tapestry appears on the wall behind the display case.
Tier 2: The Paladin. In the display case: paladin sword, book of chivalry, crisp white shirt.
Tier 3: Swords and Silk. In the display case: tessen, shuriken, sword display, urn. Fan and painting appear on the walls behind the display case.
Tier 4: Flora and Fauna of Faraway Lands . In the display case: flowering cactus, mushroom, crystal, pixie statue, ophidian mage statue, gargoyle statue.
Tier 5: May The Cards Guide Thee. In the display case: tarot cards found in a secluded gypsy wagon, an abacus found in a secluded gypsy wagon, a crystal ball found in a secluded gypsy wagon. A tapestry appears on the wall behind the display case.
Tier 6: Whimsical Momentos. In the display case: jester suit, juggling balls, jester hat.
Tier 7: One of the following: Nature's Children, There Once Ruled a Great King Over These Lands, or Of Chaos display.
Tier 8: One of the following: Nature's Children, There Once Ruled a Great King Over These Lands, or Of Chaos display.
Tier 9: One of the following: Nature's Children, There Once Ruled a Great King Over These Lands, or Of Chaos display.
The Nature's Children exhibit has a small bench in front of some sort of display. I cannot figure out what the object in the display is. Behind it on the wall are some hops with little purple lights or flowers on them that is labeled, "Decorative Vines," as well as a tapestry of some type. Very difficult to figure out what this exhibit shows.
The "There Once Ruled a Great King Over These Lands" exhibit houses an ankh and an order shield in the display case. A silver and black banner/pennant hangs on one wall next to the case and a gold shield hangs on the wall behind the case.
The "Of Chaos" exhibit houses a chaos shield in the display case. A chaos tile appears on the floor next to the display case. Two silver and black banners/pennants hang on the wall behind the tile, as well as a silver shield.
The three other exhibits that represent tiers 10, 11, and 12, but not necessarily in that order, are called, "Of Order," "Notable Villains," and "Notable Events."
Here is a stitched image of the museum room on Arirang: