This map shows the locations of the 9 kites that you collect during The Wind Will Cary Us quest and the Tethered Kites trophy. You can get the quest from Fa’zak at The Circle. The numbers correspond to both the table at the end of the post and the order they were gotten during the video. Pictures of each kite can be found at the bottom under the list.
Map of Kite Locations

Video
Individual Pictures
Table List
Video
Individual Pictures
Kite #1 – Spite Kite

Kite #2 – Transforming Kite

Kite #3 – Storm Kite

Kite #4 – Spirit of the Clan Kite

Kite #5 – Warning Kite

Kite #6 – Flower Kite

Kite #7 – Fog Guiding Kite

Kite #8 – Fight Kite

Kite #9 – Kite of Water

List of Locations
Sorry for the table width formatting, i have no control here.
1 | Mother of Rivers | Spite kite | Petrified tree on the west side of the First Zakru |
2 | Mother of Rivers | Transforming kite | Top of the First Zakru, near the entrance to the Ghost Strike Skill |
3 | Mother of Rivers | Storm kite | Tail of the First Zakru, so at the east end on the top. |
4 | Shattered Bridge | Spirit of the clan kite | Weeping Gorge area, west end |
5 | Shattered Bridge | Warning kite | On the western shattered bridge, west of Stone Blossom |
6 | Shattered Bridge | Flower kite | South of Kite String Point Na’vi Camp. In the windbent tree. |
7 | Shattered Bridge | Fog guiding kite | Northwest section of Stone Blossom area |
8 | Shattered Bridge | Fight kite | Single stone pillar in Stone Blossom area. |
9 | Shattered Bridge | Kite of water | Broken northern bit of the shattered bridge. Be careful of the stormglider. |