Here is a compilation of places where you can get map pieces.
Map board location
When you get into Origin you will see a stone building with a tower.
Behind that tower you will see a wooden door – that will be your private quarters. To open the wooden door you must complete the quests in Origin until the village chief gives you access to it.
Map piece locations
Map piece 1 is found in the cliff building south east of the River Delta teleport.
Map piece 2 is found on the first floor in a building west of the River Delta teleport.
Map piece 3 is found in the first building you visit west of the Small camp teleport.
Map piece 4 is found ontop of a strange tower northeast of the Edan Converter teleport.
Map piece 5 is found inside the cellar of the biggest house in Origin.
Map piece 6 is found ontop of a cliff southwest of the Tavar Converter teleport.
Map piece 7 is found behind the light tower near the Southern Cliffs teleport.
Map piece 8 is found inside the northern dome near the Ruins of the Dome teleport.
Map piece 9 is found in the yellow L-shape building northwest of the Crater teleport.
Map piece 10 is found inside west airdrome building west of the Hangar teleport.
Map piece 11 is found in a house west of the Company premises: Volcano teleport.
Map piece 12 is found inside the river cave near the Snow pass teleport.
Map piece 13 is found inside of a building to the north of the Southern pass teleport.
Map piece 14 is found inside a tunnel (player mark) to the east of the Domed City teleport.
Purple mark is the entry of the tunnel.
Map piece 15 is found at the bottom of the valley north of the Domed City teleport.
Map piece 16 is found ontop of the east building of a complex southeast of the South Abessa Converter teleport.
Map Puzzle completion and Rewards
When you find all map pieces, place them on the board to make it complete.
After that the safe to the right will unlock with the prizes. Hover to see the rewards:
Amulet of Wunderlust
-Max Health +10
-Frost Res +25