When and where can I find the Tower's exotic item vendor (Xur Agent of the Nine)?
Solution 1:
He's in the tower on the weekends. His position changes from weekend to weekend.
It looks like as of patch 1.0.2 Xur no longer appears on the companion app. This means that to find his location you will need to either search the Tower for him or go to your favorite game resource online to find his current location each weekend.
Solution 2:
The best way to keep track of Xur and where he is located is by using XurDay.com It's a very useful tool. You can click on the MAP tab in the top right to see where he is. Plus, you can also see what he's selling that week!