This quest can be annoying but with a bit of patience you will get it. My advice to you is to join a solo game and drop directly at an NPC that offers a disguise and buy it straight away. Then sit and wait for a player to approach. If you turn on visual sounds effects you will be able to see the players footprints and the direction they are coming from.

The busiest areas can be the best. Snow Sniper on the mountain east of Retail Row can sell you a disguise and Retail Row is a popular drop zone.

I have put a list of all NPCs that offer a disguise and where to find them below. Familiarise yourself with these so you can pick the best place to drop.

Raz can be found at Colossal crops.

Bushranger is to the southwest of Pleasant Park.

Crustina is inside The Pizza Pit just south of The Orchard.

Jekyll is inside Steamy Stacks.

Snow Sniper is to the east of Retail Row.

Map credit to fortnite.gg