There really is no easily recognizable native garb as it is a large city filled with many visitors from many different cultures and backgrounds. There would be some that would stand out a bit more then others, such as the drow for example, but the group as a whole would really not attract as much attention as what you might think.

Drow are a bit more exotic, and elves rather rare, and both would attract some curious attention but neither would raise alarm or cause any kind of unwanted stir unless the character was doing something else to provoke it.

Obviously wounded characters, or those walking around brandishing weapons, may attract some negative attention, but simply being armed is not uncommon as the city is full of mercenaries and warriors. Seeing a heavily armed and armored warrior with a peasant robe thrown over their armor may actually cause more attention, even if it is just from the fashion critics wondering why a warrior was trying to pass themselves off as a peasant.

Since many in Asgra dress to impress (even if done on a limited budget), trying to dress down may actually make you stand out even more. Asgra is a fairly prosperous city so hardly anyone is walking around in burlap dull gray peasant robes. Robes are more common among religious orders, or wizards, and they are hardly simple, at least not in most cases.