In the epilogue, James asks if Teddy can move in and says he and Albus will share a room. Harry says no because he doesn't want the house destroyed. All this suggests that they live in a fairly modest house if they don't have a spare bedroom. Albus doesn't seem to know why everyone is staring at Harry, so they possibly live in a Muggle area. For some reason I don't think they live near Ron and Hermione because they made their own way there instead of arriving together (Ron drove - LOL)
His house: As a 'famous person', would Harry have a large house? A normal one because he was trying to make his kids' life normal? Would it have a bottom floor that was always perfect for parties/such he has to host, with upstairs as his real house?
I can't see him being childish. He's seen what spoiling does to a child, and he's also seen what responsible parenting does for children via Molly and Arthur. As Maple says, he's close to Al and seems to be able to relate to all his children with love and responsibility.
It's always hard for me to write Harry in the next generation, because I'm not sure if he's funny and rather childish, because he lost his childhood and whatnot, if he's always working, or if he's a normal father. (Can be angry but can also be fun -> but not childish) I guess what I'm trying to figure out is how Harry would interact with his children.