* The animal: /ˈbʌfəloʊ/ (rhymes with "buffalo")
* The city in New York: /ˈbʌfəloʊ/ (rhymes with "buffalo")
* The verb meaning "to overwhelm": /ˈbʌfəloʊ/ (rhymes with "buffalo")
So, the pronunciation is the same in all cases, but it's worth noting the different meanings.