不用啊,里面指明地点的是the Palace Museum,在句中做宾语,不是状语,所以应用what提问:
what did Tom visit last month?
地点短语只有前面有介词的情况下才能用where提问.比如:
Tom visited his friend at the Palace Museum last month.则可用where提问:
where did Tom visit his friend last month?