Where is the painting located? What lines indicate its placement?
The first line indicates that the painting of the duchess is hanging on a wall. The Duke describes the painting, saying, "there she stands." This suggests that it is a full-length portrait, showing her standing. Perhaps it is even painted to scale, meaning that it is as tall as the duchess was. Therefore, the painting would have to be hung at least at eye level and perhaps even higher.
Near the end of the poem, the Duke repeats, "there she stands / As if alive." This adds more support to the idea that it is a full-scale representation of the duchess. The Duke then says that they shall meet the company "below." So, the painting is upstairs somewhere. This does not necessarily mean that it is precisely at the top of a flight of stairs. They might be in an upstairs room with other paintings and/or heirlooms. This would fit the Duke's arrogant and showy personality. The Duke would invite people to such a room in order to show off his possessions. Possession is a fitting word here in that he also treated his wife like a possession.
The action when the painting is shown to the ambassador "nay, nay, we'll go together down" implies that the Duke is giving a tour of the upstairs of his mansion, and he and the ambassador are going downstairs and have reached a landing -- "Twill please you sit and look at her?" So it appears that the painting is curtained, on the landing."