Domestically, orphanages do not exist in the traditional sense. The United States has a complex foster care system which aids in the developmental care of children placed temporarily within family homes. You can read about the history of the country's movement from traditional orphanages to the foster care system here: https://adoption.com/wiki/End_of_American_Orphanages . While the foster care system has a primary goal of caring for children, placement is often temporary. Children in foster care are rehomed for a period of time when their own family is unable to care for them. Many foster children return to their families of origin once appropriate measures, often court ordered, have been made to ensure the safety and functionality of the home and therefore the future safety of the child. It is when a foster child is unable to return home that the child then becomes adoptable. If your intention for "visiting orphanages" is to learn about children who are adoptable through the foster care system, you may call your local department of social services or begin with this link: https://www.adoptuskids.org/meet-the-children/search-for-children/state-photolists.
Internationally, orphanages exist but are a growing "voluntourism" problem, meaning the infrastructure of such caring-giving institutions have fostered an environment of tourism revenue and child exploitation in some countries. Parents of poorer families are often pressured into putting their children into these orphanages for the purposes of education and proper nutrition, but these children do indeed have families. Here's an editorial on such practices with activism tips. http://www.abc.net.au/news/2018-01-31/improving-orphanage-voluntourism/9375614.
All this to say, if your intention is to visit international orphanages, do your research. Adoption and volunteerism is a wonderful thing; to participate in the exploitation of children is not. Unfortunately, political unrest and economic instability can cause people to do amazingly wrong things, even under the veil of caring for children. Find a legitimately recognized international aid organization or faith-based effort to work with, one who has a history and relationship with the orphanage with which they are partnered. Ask questions with wisdom. Where do these children come from? Who are their parents? Are they alive? Why are these children here?