Entry location: All Levels
When you go across the edge while chasing the deer, look right and you'll see a ledge. Jump and you will find the egg.
Just after you kill the soldier with your bow in the smithy, there is a wooden plank hanging off the ceiling. Climb it and keep going until you can climb up. The egg is up there.
When you have climbed across the mast, instead of running up, keep on going and soon enough you will find the egg.
When you have knocked aside the wooden planks that fell from the ceiling, there is a balancing beam. When you get across you will see the egg.
When the bridge is knocked down and landed on that guy, and when you've jumped down from the next part of the bridge, go across to just before Eragon learns the fire arrow. When you jump down, you will see the egg.
When you reach the first massive opening, when you go around to the left, fly low so you can see everything. Just under the waterfall, the egg is waiting just in that.
Run to the back of the arena, the egg is just near the rocks.
This one is tricky, but when you have opened the first gate, head left and climb the ledge. Run across until you fall on the ledge where the egg is.
When you have crossed the keep maze, go down on the other side of the maze and you will see the egg.
The is quite tricky, but if you search every staircase of every level (I believe that is on one of the lower levels) you will find the egg.
The Beor Mountains
When you have crossed the bridge after fighting in the water, (when you have to call Saphira) and when you have reached the last spot, look up on the top of the cliff, the egg should be sitting right there.
When you get to the place where you can use the spears with ur magic, go left and jump down the edge. Viola, there it is.
When you have finished the big fog bit, and uve reached the maze,look on the west side at the bottom. The egg is there.
Fly over one of the edges where the urgal arches fire at u, fly over them and the egg is in that section.
Defend The Varden
When you go across the massive bridge, go downstairs where the middle is, and there is the egg.
This is all up to chance, you just need to be on the look out for the egg coming at you. It could be at anytime that it comes so just be ready.
Unlocking all of the eggs will let you have access to the making of Eragon. Also, it will let you go to the Throne Room and fight Durza's endless army.