I also got introduced to the amazing sweet carbonated beverage Peach Nehi at a friend’s house. Of all the Nehi flavors, peach was always my favorite. Peach Nehi ice cream float….(!!!) If Peach Nehi holds a special place in your heart, a road trip to Scott’s Iconium is in order. LOOK: The 21 most popular ice cream flavors in America Stacker analyzed YouGov data and found the most popular ice cream flavors in the U.S. Read on to find America's favorite flavors.