Whilst the gold punch cards don't actually get you anything in particular (there are no achievements or unlocked content attached to them), they do each give you a little extra background and lore about the world.

Annoyingly if you finish the game and start over on the same profile, while it does remember your previously collected cards, it then treats each card you collect in your new play through (including duplicates) as a brand new card, meaning you can end up with 30+ out of the possible 29.

The game is divided into areas so I've included the number found in each area as well as your starting/ending totals for an area in case you want more of a nudge rather than just being handed the solution.

In general zoomable areas containing cards will remain active until the card is collected even if all the other game elements are completed or collected, however some are missable even within the chapter so I've tried to flag these specifically.

There is 1 card to be found in this area.
You should start this area with 0 cards and end with 1.
This area is exited when you press the switch in the elevator.

1. Bedroom - "Professor Stone" - Zoom on the table in your bedroom
   
   

There are 5 cards to be found in this section, one of which is missable.
You should start this area with 1 card and end with 6.
This area is exited when you press the lever in the helicopter.

1. Foyer - "Memory Crystal" - MISSABLE - Zoom on the bookcase on the right, below the box of minerals. Inaccessible once the bookcase is open.
   
   
   
   
2. Foyer - "Tree of Stone" - Zoom on the vault in the wall. Bottom left , under the switch.
   
   
   
   
3. Study - "Hollow Earth" - Zoom on table on the left, in the drawer where the lens is found.
   
   
   
   
4. Hangar - "Hyperboloid Ray" - Zoom on Desk. To the left of the panel.
   
   
   
   
5. Hangar - "Mystery of the Himalayas" - Zoom on helicopter. On the dashboard.
   
   

There are 4 cards to be found in this area.
You should start this area with 6 cards and end with 10.
This area is exited when you solve the engine puzzle in the subterrene.

1. Exterior - "Olivine" - Zoom on Olivine can. Wedged under barrel on left.
   
   
   
   
2. Exterior - "Beings from SIRIUS" - Zoom on buried arm. In snow in foreground.
   
   
   
   
3. Interior - "Robot Samson" - Zoom on Table under lamp on left. Wedged under box.
   
   
   
   
4. Subterrene - "Subterrene" - Zoom on the map on the right hand side. Stuck to the wall on the top left.
   
   

There are 3 cards to be found in this area, 2 of which are missable.
You should start this area with 10 cards and end with 13.
This area has multiple exit triggers as you complete it when you have finished setting everything up to be as it was when you visited earlier.

Completing the puzzle behind the grill (left side) of the hangar will cause the hangar/lab area to be closed off the next time you exit to the house and completing the remaining house tasks will trigger the next cut scene. Most of these can be completed before this, (power off, stashing the voice cylinder/hangar remote, burning the blueprint, making the film) other than hiding the blue gem since that falls out of the secret door to the hangar when it closes. As there isn't a set order though, whichever you complete last will trigger the end of this chapter.

1. Study - "Stone’s Fortress" - Zoom on box by sofa. Hidden under newspaper on sofa.
   
   
   
   
2. Lab - "Hidden talent" - MISSABLE - Zoom on voice recording device. Lodged slightly under the device. Only available before you close the entrance to the hangar.
   
   
   
   
3. Lab - "Count Stauffenberg" - MISSABLE - Nestled in the red box on the left. Only available before you close the entrance to the hangar.
   
   

There are 6 cards to be found in this area, one of which is missable.
You should start this area with 13 cards and end with 19.
This area is exited with you pull the lever on the portal machine.

1. Sleeping Area - "Free servants" - MISSABLE - Zoom on cupboard on the right. Hidden behind paper containing formulas on the left hand side. This area is off limits after the explosion.
   
   
   
   
2. Hallway - "New Hope" - Zoom on outfit. Tucked into waistband.
   
   
   
   
3. Storage Room - "New Hope Headquarters" - Zoom on box to the left of the door. Wedged at front of box.
   
   
   
   
4. Count’s Lab - "Crystal Skulls" - Zoom on crystal. Leaning against crystal. Can be grabbed with crane.
   
   
   
   
5. Count’s Lab - "The flip side of virtue" - Zoom on low cupboard. Wedged in folders.
   
   
   
   
6. Security Room - "Hyperboloid accident" - Zoom on left surface. Behind clipboard.
   
   

There are 10 cards to be found in this area.
You should start this area with 19 cards and end with 29.
This area is exited when you complete the marble/maze puzzle.

1. Wrecked Cockpit - "Travel beneath the surface" - Zoom on radar. On top by switches.
   
   
   
   
2. Subterrene Living Room - "Hidden ancient monoliths" - Zoom on the city in the middle once the forcefield is deactivated. Stuck to the outer edge of the stand.
   
   
   
   
3. Entrance - "Victims of olivine" - Zoom on left statue. Below the head.
   
   
   
   
4. Entrance - "Guardians of clarity" - Zoom on right statue. On right side of base.
   
   
   
   
5. Crystal Cave - "Breath of Agartha" - Zoom on central device. Right side of pedestal.
   
   
   
   
6. Crystal Cave - "Icy Gems" - Zoom on blue crystals. Partially behind crystal on right.
   
   
   
   
7. River Cave - "The handiwork of the masters" - Zoom blue doorway. On the ground on the right.
   
   
   
   
8. Underground Jungle - "Where else can life exist?" - Zoom on the pinkish cave. Top left behind the matching flower mini game.
   
   
   
   
9. Underground Ocean - "Fantasy and skepticism" - Zoom on the observation plateau. On the right of the viewing machine.
   
   
   
   
10. Underground Ocean - "Gods, aliens or elder brothers" - Zoom on the saucer type structure. On the desk on the left hand side.