Japanese Prime Minister Noboru Takeshita left Tokyo for Washington for his first summit with President Reagan, seeking to cement a partnership troubled by trade friction. Before departing, Takeshita said he hopes Reagan will understand that "Japan is a good partner of the United States. . . . It is important for me to establish a close personal relationship with the U.S. President." Takeshita, 63, who became prime minister Nov. 6, will meet with Reagan on Wednesday. He is also scheduled to meet with members of Congress and deliver a speech at the National Press Club.