He's the Absent Creator
The simplest answer to Dr. Manhattan's whereabouts can be found at the end of the graphic novel. Disillusioned with humanity, he decides to leave Earth, explore the galaxy, and perhaps create life. If the live feed from Mars we see in episode one is to be believed, he has settled on Mars and abandoned the human race for good. Another hint pointing to this is Adrian Veidt's comment to the clones in his bizarre prison world. Veidt claims their creator has left them behind, indicating Dr. Manhattan might've experimented with lifeforms, just as he said he would in the graphic novel. For some reason, things didn't go as planned, and he gave up on them.