Most of the hotel is constructed on the site of the old Palace Hotel.
Here's a description they provided:
...The old Palace Hotel was originally built in 1928-1929...on the initiative of the Supreme Muslim Council, under supervision of the Mufti of Jerusalem and during the term of Raghib Nashashibi, the British-appointed mayor of Jerusalem...designed by Turkish architect Nahas Bey and built by one Arab and two Jewish contractors, [it] was completed in a record time of just eleven months by over 500 Arab workers...
...The Supreme Muslim Council soon found that they could not keep up with the financial load of the hotel and they leased the hotel to hotelier George Barsky, who could not compete with the nearby King David Hotel once it opened in 1931.
The Palace Hotel was then turned into administrative and military offices of the mandatory government. In 1937, the Royal Peel Commission, which recommended the partition of the area, assembled in the hotel. During the British Mandate (1945-1948) the Palace served as military and administrative offices...
They left out that it was build on a part of the Mamilla Cemetery which presented no problem for the Mufti, unlike the problems the Waqf forces on the Museum of Tolerance.
The eastern wing of the new hotel was constructed over the site of the former Tax and Excise Office which became a museum.
That building, at the corner of Agron and King David Streets, was, in 1946, the headquarters of the 'Jerusalem District Income Tax Office on St. Louis Way'. And on November 20, 1946, it was attacked by the Irgun who inserted the explosives in a trolley as if visiting cards were being delivered,
Here is a clipping from the Palestine Post the next day:
Shmuel Tamir commanded the operation.
On February 27, 1944, the Tax Commissioner's Office was attacked:
I am not sure if that was a different building at another location, further up towards today's Zahal Square, opposite and diagonally across from the Mamilla Hotel.