I would tell him face to face that you have had so much on your mind and you were unable to make it. I am sure he will understand. You do not want him to wonder why you did not show up. But you do not have to tell him you forgot. You want to simple tell him that you have a lot on your mind.
He will understand because he as well has a lot going on in his life as well.
He already moved, actually. What if I can't tell him to his face?
I feel that you should send him an e-mail and explain why you were not there at the party. But also ask him how he is doing settling in. It would be nice for you just to check in to see how he is doing so he knows he has support through this huge change in his life.
Great - thank you!