The Partridge Family was a well-known enough group to obtain a booking at King's Island amusement park across the country from the California home, but not wealthy enough to travel in a chauffeured coach or even by air to most of their other gigs.
Either they are a minor local group or they are nationally known; the two cannot both hold true.
The interior of the Partridge home was shot on a set. But, in episodes where there are shots from the exterior of the Partridge home through the open front door, there is a wall seen a few feet beyond the door. However, in the scenes from the interior of the home, there is no wall in that spot.