There is a spot, the perfect spot if you will, where you can get upwards of 30 eggs in 15 minutes. More if you're not bothered by others attempting to rain on your egg parade.
The spot exists in Azure Watch outside of Exodar, and I've gotten a few pictures you can see after the break to make it easy for you to sit there and farm away for a bit. While this trick won't necessarily work in the early evening when everyone and their mother's uncle is on farming eggs, it works great during off hours.
When you're there, you'll notice a big rock surrounded by two smaller rocks. Position yourself next to the left most rock near right near the shrub. There's an egg in the shrub and an egg behind the big rock that you can click on from that location without having to move.
Zoom your camera out.
In front of you, you'll notice a large crystal, and to the right of that crystal you'll notice a little stand with some junk. There are two eggs which spawn there. One egg spawns at the base of the crystal.
And to the extreme left of you, you'll notice a building's wall with a tree near it. Two eggs spawn right next to one another near the tree and wall.
What you want to do is sit at the original location (47, 50) and move forward to grab the eggs in front of you, then back to the original location. Then move to the left to get the eggs over yonder, and then move back. Rinse and repeat, all the while farming the egg in the bush and behind the rock, and you'll be quite happy.
If you've got a lot of runners around you (people who run all over the place looking for eggs), then leave the two to the far left for them. That way they'll think you're afk or just dumb and not bother you with the other spots you're secretly farming. It's the whole "Keep your friends close and your enemies closer" mantra.
That's it. You're my friend. Come here and close your eyes, let me give you a hug.