This building in Old Town Historic Park was built in 1827, and now has period furnishings to illustrate the way its rooms would have appeared then. I do not know whether the furnishings are authentic or reconstructions, though I suspect the latter. There is also an interesting semi-enclosed garden with cacti and other native plants of that area. This is the centerpiece of Old Town, and worth a special visit just to see it.
One thing that was not mentioned by the interpretive staff or in the literature I saw in the park - This place has the reputation of being the most haunted spot in San Diego. In particular, so the story goes, don't look in the mirrors in the building unless you are prepared to see some faces besides your own looking back out at you!