A latchable room is a room that allows the entry portal - generally a door - to be locked from the inside by use of the LATCH verb.
The following is a list of known latchable rooms.
(H) = must be a house member to access
(P) = publicly accessible
Firefly Villa - six latchable rooms upstairs (P): The Silver Room, The Saffron Room, The Purple Room, The Blue Room, The Green Room, The Azure Room,
Note on Firefly Villa: In these rooms there are two doors that need to be latched - one to the outside hall and one to a shared balcony.
Scuttlebug Tavern - two latchable rooms upstairs (P): Grey Room, Red Room
Frith's Inn - two latchable rooms upstairs (P): Boudoir, Bedchamber
Raging Thrak Inn - one latchable room upstairs (P): Suite
Hearthstone Manor - two latchable rooms upstairs (P): Rose Room, Guest Room
Note: While Hearthstone Manor is open to the public, there is a minimum fame requirement to enter.
Silvergate Inn - bathroom (H), several other latchable rooms (P)
House Brigatta - three latchable rooms (H)
House of the Rising Phoenix - three latchable rooms upstairs (H)
Obsidian Tower - seventeen latchable rooms upstairs (H)
Clovertooth Hall - one latchable upstairs (P): Conference Room
Honeybeer Inn - two latchable rooms upstairs (P): White Room, Maoral Room
Thirsty Penguin - two latchable rooms downstairs (P):Snow Room, Blue Room
Captain's Rest - latchable rooms upstairs (P)
Wage and Dagger - two latchable rooms upstairs (P)
Bathhouse - several latchable bathing rooms (P)
Solhaven Inn - several latchable rooms (P)
Trading Post - several latchable rooms (P)
Krawling Kraken - Sitting Room, Scaled Room, Pine Room, Cozy Room, Trophy Room, Sailor's Ease, Seascape Room (P)
Bawdy Bard Inn - four latchagle rooms downstairs (P):Horn Room, Strings Room, Percussion Room, Woodwind Room
Tregg's Tavern - two latchable roooms (P)
Note: This is in Khazar's Hold, which is before Zul Logoth, to the west side.
Feystone Inn - near Sylvarraend, two latchable rooms upstairs (P): Sitting Room, Bedroom
Shimmarglin Inn - ten latchable rooms upstairs (P): Charging Boar Room, Twisting Serpent Room, Mountain Peak Room, Bright Berry Room, Red Bear Room, Yellow Sunburst Room, Soaring Falcon Room, Black Oak Room, Timber Wolf Room, Wood Sprite Room
The Legendary Rest - four latchable rooms upstairs (P): Lofty Peaks Room, Sea N' Shore Room, Desert Evening Room, Golden Harvest Room; three latchable rooms downstairs (P): Forest Clearing Room, City Life Room, City Vista Room
Malwith Inn - three latchable rooms upstairs (P): Green Suite, Blue Suite, Bedroom