It's been 2c three times in the past, but I suspect your card was mailed in the 1952-59 range. Of course, the pictures could show the hotel many years earlier than the date mailed.

1872 (1 cent),
1917 (2 cents),
1919 (1 cent),
1925 (2 cents),
1928 (1 cent),
1952 (2 cents),
1959 (3 cents),
1963 (4 cents),
1968 (5 cents),
1973 (8 cents),
1975 (7 cents),
1976 (9 cents),
1978 (10 cents),
1981 (12 cents),
1981 (13 cents),
1985 (14 cents),
1988 (15 cents),
1991 (19 cents),
1995 (20 cents).