NOTE: The heading for each entry is the location you are trying to find the Gate Seal for, not in. I do this because I assume that you are looking for a Gate Seal to close a certain location. For instance, if you want to find the Gate Seal to close New Bodhum 3AF, do you really want to search each areas description or just find the heading for the one you want. Keep that in mind to avoid confusion.
New Bodhum 3AF - In Bresha Ruins 5AF, go up the stairs towards the Time Gate you got here through. Go up the stairs going right and you should find this at the top, around a corner.
Bresha Ruins 5AF - From Chocolina's Shop in the SW part of the map, you should be able to see this to the right of one of the lamps. It should be in the NW most part of the plains, N of the spotlight area.
Yaschas Massif 10AF - the building in the middle of town, SE from Chocolina. You should find this inside the building.
Yaschas Massif 1XAF - In Serendipity, you will find this just N of the Sage's house and W of the giant Roulette wheel.
Oerba 200AF - In Yaschas Massif 1XAF, head S out of the ruins and follow that path straight down to the end. It will lead you to a cliff that you have to jump down a few times as the path curves E.
Sunleth Waterscape 300AF - In Academia 400AF, you'll come across a Chocolina Shop next to the woman who starts the Map exploration quest. In between them should be this Gate Seal.
Archylte Steppe - You must get this during your second visit to the Void Beyond or time reverse Sunleth Waterscape 300AF to replay the Void Beyond. It will be in the NW corner of the map.
Coliseum - You must get this during your second visit to the Void Beyond or time reverse Sunleth Waterscape 300AF to replay the Void Beyond. This will be in the SW corner of the map.
Academia 400AF - In Oerba 300AF, This is SW of the schoolhouse. From the location where you throw Mog to get the Wilde Artefact, you want to throw Mog again. This time, you want to "miss" off the right side and a little closer to you.
Academia 4XXAF - This gate seal is in A Dying World 700AF. You will find this Seal as you are walking towards the Oracle Drive through the settlement. On the way, you'll pass a little open area behind a wall and this cube is hidden behind the wall.
Augusta Tower 200AF - This Seal is in Academia 4XXAF. Go into the Academia HQ. You'll find this Seal behind the reception desk, requiring you to throw Mog to it.
Augusta Tower 300AF - This Seal is in Augusta Tower 200AF. Off the SE part of the 51st floor, you'll find a floating Treasure Cube. You'll have to throw Mog over to it.
A Dying World 700AF - This Seal is right by the spot where you come into Academia 500AF, slightly to the NE.
New Bodhum 700AF - You'll find this on a platform just E of the spinning T platform in the middle of the map and NE of the longest horizontal platform.
Bresha Ruins 100AF - This Gate Seal is actually in Bresha Ruins 100AF and is in the Control Device room. Check the SE corner with a Moogle Hunt to find it.
Bresha Ruins 300AF - This Seal is also in Bresha Ruins 300AF. This Seal is just to the E as you come into the area. Use a Chocobo to jump the wall. This is the area where you found the Graviton Core in 5AF
Yaschas Massif 100AF - You get this Seal in this very timeline. Stand at the top of the ramp next to Chocolina's Shop and look down over the W rail. You should see the box. It's very close but inaccessible so you'll have to throw Mog.
Yaschas Massif 110AF - This Gate Seal is actually up by the Statue Head in the Acropolis.
Oerba 300AF - In Oerba 300AF, there is a ramp N of Chocolina. Go up the ramp and at the top, take a couple of steps N. Now Look E and below you. Along the side of the ramp you just came up will be a bunch of boxes. Throw Mog down to them to collect this Seal.
Oerba 400AF - From Chocolina, take the ramp that leads down a level. Just to your left, you should see a massive gnarl of roots that lead up a little above you. Atop this roots, in an area that you can't reach, is the treasure cube with this seal. Throw Mog up to it.
Sunleth Waterscape 400AF - You get this from defeating the five miniflan and obtaining the Miniflan Fragment.
Vile Peaks 10AF - You'll get this Gate Seal after defeating Twilight Odin twice. Once here and then once in 200AF. See the Vile Peaks are of the Fragment Section for more details.
Vile Peaks 200AF - You'll get this Gate Seal after defeating Twilight Odin twice. Once here and then once in 200AF. See the Vile Peaks are of the Fragment Section for more details.
Serendipity - You'll find this in the Bresha Ruins 100 AF time period. Go to the area that had the N most gate in 5AF (it's about the center of the map with a lot of pillars). This gate seal is on the W wall.
Academia 500AF - This Gate Seal is on the last platform before you get to the Academy HQ. This platform has a Green cactuar statue and a red cactuar statue. The Seal is on this platform on the E side.
Valhalla - Complete the main story