I had already written an answer to a similar question.
If one makes a general survey, s/he would find it is rarely common in Iran for Muslims to holds images of holy figures in their homes. This is more true for Prophet Muhammad. Still you may come across images of Imam Hussein (as) or Abbas ibn Ali (as) in Hussaynias but even this is not very common.
Among my own associates, I only remember my maternal grandfather's who were not educated Muslims to hold an image of Prophet Muhammad (as) in their living room. To the contrary I never saw my paternal grandfather who was a very pious and studied cleric to do this. But instead he had a Hussaynia in his village where during the Month of Muharram, moving depictions of Karballa tragedy where shown on the walls with the faces of Hussein, Abbas, Zaynab and other respected figures (pbut) in the event opaqued with a shade of light.
These were artistic professional depictions which have been to the contrary an accepted practice in Iran and among Shias in general. But still these creations are not widely published and distributed among the people. They are reserved mostly for art galleries and museums, while you may find some Husaynias using this on the walls like my grandfather's.
The artistic depictions are done mostly in the spirit of reverence for these holy figures and the Shia scholars approve of this so long as it is done in a dignified style, with due care for religious sensitivities, promoted with reservation and kept within limits.
Two Iranian artists who have done particularly amazing works for the Islamic holy figures in Iran are Mahmoud Farshcian whose breathtaking style is unique in its kind. Among several of his works with mystical themes, there are a handful that depict holy figures without showing the faces.
A more recent example is Mohsen Ruhul-Amin, a young talent artist with mostly depictions of tragic chapters in Shia history.
I also know of a unique case which shows that despite this allowance, religious considerations are still kept up. In this link you can see a depiction of Ali (pbuh) by an artist who has claimed to have seen the figure in a dream. The depiction reportedly closely parralles historical reports about the looks of the Prophet's cousin and son-in-law. However since the idea of a portrait based on a true vision can be controversial, this painting remains widely unknown in Iran and you find it featured online to this date by only two junior Persian news websites. The work is now in the possession of Astan Quds Razavi Museum and they personally told me that they don't like it to be promoted.
So as you see there's a culture that while doesn't approve of widespread display of images of holy Islamic figure, it still allows chances for genuine expression of religious devotion for saints in form of art. These reservations are less strict for non-Islamic holy figures such as Israelite Prophets as I have explained in the answer I linked in the beginning of my answer. This situation reflects ijtihad of the mainstream Shia scholars. There's still an orthodox minority though that forbids any depictions of humans be it saints or other similar to the Sunni and Salafi clerics.
If you are interested in personally visiting these works, other than Astan Quds Razavi in Mashhad you may want to visit Sadabad Palace Museum for Fine Arts in Tehran. Among Farshcian works I remember a depiction when Prophet Muhammad is feature next to Ali in the context of Ghadir Khum. But I don't know of any museum or gallery dedicated exclusively to depictions of Prophet Muhammad since there have been few such works.
