The proper question isn't so much "what" but "when" Psyren is five years in the future. It is North America but an event happened (thanks to WISE) that caused the world to become nothing but a wasteland void of life except for the lucky humans and the Tavoo. To get a good mental image of what Psyren looks like picture this:
A desert. Now add some dunes, a couple cliffs, remove plant life, and add the occasional ruins. Throw in a ton of very tall, foreboding, and high tech looking towers as well as clouds that block out the sun (but allow light to pass through), and now you have Psyren.