Just now I watched this video about the attempted Mongol invasions of Japan.
I guess that Japan with its foresty mouintains would be difficult to invade for the Mongols who would probably favor open plains. So finding a good spot to land would be especially difficult for them.
But why did the Mongols attack the Hakata Bay area with its fortifications twice? To me it seems to be a particularly bad spot. More so in 1281, after the Japanese enhanced their fortifications and conveniently(?) guarded the area with an army.
Though it would be definitely better to wait for responses either from the Mongol History or Japanese Medieval Historians, I just complement some brief historical background around two Mongol invasion attempts as well as some facts on the Japanese-Chinese(-Korean) sea trade across the East China Sea in the 13th century that I assume relatively less known out of East Asia.
Put it briefly, contrary to OP's supposition, the majority of Japanese scholars tend to point out the general overestimation of the Mongols as a sea power at that phase (ca. 1280), and regard the NW Kyushu around Hakata Bay as an only realistic destination of the fleet. Their reasonings are as following:
References: