"He is going to Paris."
Translation:Er geht auf Paris zu.
Yes, not correct, even big wrong. If you are in one city to one city, for example Berlin to Paris, the you should using "nach". And the verb it self also wrong, it should be either "fahren" or "fliegen". So, from what I understand, the correct sentence, it should be "er fliegt nach Paris". If you are intented to go to bed from living room, then you can write "ich gehe ins Bett" - I am going (walking/by foot) to bed/ to sleep