I'm near positive your vault will be the same size no matter how big your house is.
The places to look for bigger rooms are the main town districts, not the suburbs. North Qeynos has an inn with bigger rooms, and South Qeynos is full of expensive houses, all down the streets. As for Freeport, I can't recall which districts have houses and inn rooms, but it'll be North, South, East, or West Freeport.