Altar - particularly if the statue is on a small shelf, table or pedestal and especially if flowers are placed there
Grotto – when the statue is sited in among rocks and a small garden
or perhaps Shrine
In Maine, where I used to live, it was also very Catholic. In older homes, when they would replace their old cast-iron bathtubs with more modern, installed tubs, the would dig up the ground, and put the tub in upright so about half of it stuck out of the ground. Then they would fill in around it and put a statue of Mary inside, so it looked like a little shrine. They were known as "bathtub Virgins." They are harder to find these days, but seeing one always made me smile.