MAGAZINE LOCATION SPOILERS:

INSTITUTE SKIN ("INSTITUTE LAER MANUAL" MAGAZINE):
In the Institute, in Advanced Weapons Systems, next to a terminal and the LAER lore holotape.
If the Institute has been destroyed, the magazine, holotape and LAER are moved to Fort Hagen, where Kellogg is found. (VERSION 1.1 EXCLUSIVE)

BIG MT SKIN
Requires "INSTITUTE LAER MANUAL" magazine. See above. (VERSION 1.1 and up EXCLUSIVE)

RAILROAD SKIN ("RAILROAD LAER MANUAL" MAGAZINE):
In Railroad HQ, next to Tinker Tom's LAER, over a table on the east wing of the HQ.

HA_RU'S SKIN ("LOCKER ROOM TALES" MAGAZINE)
On a bench near the lockers in the boxing place in the General Atomics Galleria.

WANAMINGO'S SKIN ("HALLOWEEN SPIRIT!" MAGAZINE)
In Museum of Witchcraft, right after you enter over a table, next to a skull and a candle.

VICYORUS' SKIN ("GRIMDARK FANTASY" MAGAZINE)
In Fort Hagen (ground floor) somewhere where a roof collapsed, next to a skeleton (look in the release trailer video).

PIE_SAVVY'S SKIN ("FLOWER CHILD" MAGAZINE)
In Goodneighbour's Hotel Rexford, in the last room in the second floor, over a briefcase (also look in the release trailer video).