There is no unduplicated count of visitors to the U.S. that are not permanent resident (green card) holders – i.e. persons who are not “immigrants.” (Green cards are issued to about one million persons a year.)
Canadians and Mexicans are by far the most frequent visitors to the U.S. For short tourism or business stays Canadians do not need a visa but Mexicans do. I cannot find an unduplicated count of these visitors, but in total annual border crossings Canadians accounted for about 104 million of the 181 million border crossings in 2016, according to the Congressional Research Service.
Aside from Canadians and Mexicans, about 22 million persons enter legally through the Visa Waiver Program, available to citizens of most developed countries, allows visitors to travel to the United States for tourism, business, or while in transit for up to 90 days without having to obtain a visa. The countries with the most visitors in this category are the United Kingdom, Japan, Germany. France, Australia and Korea.
Then there are about 10 million persons who receive one of 24 different temporary visas generally allowing them to stay more than 90 days. They are commonly referred to by the letter and numeral that denote their subsection in the Immigration and Nationality Act (INA); for example, B-2 tourists, E-2 treaty investors, F-1 foreign students, and H-1B temporary professionals. Eight of the 10 million come for business or tourism. About two million come in special categories, such as (2016 figures) were temporary workers (883,000), students (513,000), and cultural exchange visitors (380,000). Visas issued to foreign nationals from Asia made up 45% of these visas issued in FY2016.