Missiles are hard to come by as the majority of such ammunition is found by killing enemies that utilize the missile launcher. These enemies are limited to super mutants, higher-leveled Talon Company mercs, raiders, and some wastelanders. Even though these are common enemies, few members of such groups carry a missile launcher at low levels (level 2-14).
Flak 'N Shrapnel's will carry around 3 missiles for sale, but this supply will rarely exceed 6 missiles.
Lucky Harith carries up to 20 missiles at a time when the player invests a second time in the free-form quest Merchant Empire.
Traveling to the extreme south-east corner of the map, near Rivet City, you can find 2 ammunition boxes exclusively containing missiles on the wreckage of a ship. You will have to swim across the river to get here.
Over 28 split across three ammunition boxes on a wrecked barge just west of Arefu along the shallow river bank. (Confirmed with Scrounger only).
Three on the ground and in an ammunition box next to a missile launcher around the back of the Washington Monument.
Sometimes, the player can randomly find missiles on enemies that do not use a missile launcher.
A player can find more missiles in ammunition containers with the ScroungerPerk. Combined with high Luck, there have been cases of players finding over 30 missiles in one container.