I know this is not in the book, but what house would he be in? His dad was in Gryffindor, his mom in Hufflepuff, and his grandmother in Slytherin. So what about Teddy?
i could see him takeing after his mum in the im awesomely cool and loopy
and i could see him being extremely kind and caring and brave and mischievous like his dad
Personally I think he was a Ravenclaw because if you think about it, Tonks was smart enough to be an Auror and Remus was a very bookish, clever kind of person. Combine those two and you've got a Ravenclaw, born and bred. Then again Ravenclaws obey the rules. Tonks was said to have been a likeable person but she liked to party. Remus was a Prefect but he was also a Marauderer and it was said that he never really enforced the rules around James, Peter and Sirius for fear of loosing them.
On the other hand, he could have been a Slytherin as he is related to the Blacks through his grandmother: Andromada Tonks (ne: Black) who was Narcissa Malfoy and Bellatrix LeStrange's sister.
I doubt that Teddy would be a Hufflepuff as Hufflepuff's are often happy-go lucky people and I don't think that Teddy would be like that as he would have to had delt with the fact that his parents died and that he never could speak to them or get to know them. I believe that he would be like Harry just without the OMGLordVoldemortisgatheringahugearmytotakeovertheworld! And the angst. He would have angst just not as much as Harry. Neville-sized angst lets say.
He could be a Gryffindor I guess. I only say this because I have no arguments against it.