Depending on where you are in the area, and which area you are in, there are generally 2 - 3 spawn locations for invasions. They are generally in obvious locations, and depending on where you are in the area, determines the location in which they will spawn. eg, if you are in the beginning of the area, they will spawn in the first location.
They will not spawn further than the closest fog gate. i.e; if you have just entered an area, the invader will not spawn behind the first fog wall.
Unfortunately, in areas like Dragon Aerie, with lots of narrow winding paths, it's possible to easily lose the other player, or in your case, never find them. Generally the best way to locate each other is to find a large, open area, possibly send a message letting them know where you are.
However, I can't answer your question completely with a list of pre-determined spawn locations until I have done some further research.