Usually where all the shops are in the cities. But the name of the shop is different for each city. In Limsa it's called the Dyemonger near the arcanist guild. In Ul'dah it's on the southern part of the ruby exchange on the east side, think it was just called independent merchant or something. In Gridania it's on the north part of the exchange on the west side below the lancers guild.
From a Dyemonger. TBH we need more mongers IRL. Apart from fishmongers I don't know any others. Par Exemple Burgermongers for grub / Carmongers for motors/ Techmongers for your gadgets / Lootmongers for your swag.