Below is a full list of trade locations. Sales can be conducted within the appropriately marked subforums. I've added quick notes where I thought they'd help further understanding.

This information is subject to change, and efforts will be made to keep this list updated with any changes as they arise.

HAN
Huan Shu – Armory for Pikes and Spears
]Ting Pang – Bow Armory, Market
Mang Zhuan – Siege Factory (ram, catapult, tower siege weapons for company outfitting), Market
Wuhu – Naval and Boat Yard (ship and warship production; ship moves fast and carries little, while warship is larger, carries more, and is far slower)
Jian Ye – Naval and Boat Yard (see above)

SONG
Mingde – Market, Stable (horse sales)
Ping Shuang – Blacksmiths (buy and sell weapons and armor), Armory for Spears and Swords (outfit troops with spears/swords)
Yu Shuhan – Stable (see above)
Chen Liu – Siege Factory, Market
Hong Ling – Market

CHU
Han Ming – Farms (all crops grown here, largest food producers, dig for valuable items here), Market, Armory for Swords (some of best sword quality in the land; all kingdom swords made here; specialty swords available for considerable price)
Shu Hanlu – Siege Factory
Cang Yang – Elephant and Beast Master Armory (only place in the land to acquire elephants and beast masters for units)
Bingzhu – Armory for Bows and Pikes (equip units with bows and pikes), Blacksmiths (buy and sell weapons and armor)
ChengDu – Siege Factory (siege weapons – unique to Chu are juggernauts and arbalests), Bow Armory (outfit troops with bows and arrows), Market

TIAN GUO
Zhong Xin – Treasury (ruler and trusted officials access kingdom wealth, weapons, and fine armor), General Armory (outfit troops with spears, swords, pikes, or bows), Market
Kai Tie Jiang – Blacksmiths (any weapon type made here; fresh ore supply leads to plentiful availability of weapons, though exceptional quality is still expensive), Bar (for officers to relax; buy alcohol and other pleasures), Mines (long, stretch under the entire city, no threat of collapse; ore comes from here; officers can mine their own ore to forge weapons or sell for gold)
Yu Min – Naval and Boat Yard