If you mean at the same time, obviously Chicago and New York. If you mean just 2 different teams that is a whole different can if worms. This is a partial answer. There have been many cities that have had two MLB teams at the same time.
1) Philadelphia - Athletics (1901-1954), Phillies (1883-current)
2) Boston - Red Sox(1901-current), Braves (1876-1952)
3) St. Louis - Browns (1902-1953), Cardinals (1892-current)
4) New York - Yankees (1903-current), Giants (1885-1957), Dodgers (1890-1957) Currently Yankees and Mets(1962-current)
5) Chicago - White Sox (1901-current), Cubs (1876-current)
6) Los Angeles - Dodgers (1958-current), Angels (1961-1964)