Percy does not really yearn for any beautiful women in The Lightning Thief. He admires Annabeth's intelligence and perceives her as being attractive, with her long blonde hair and startling gray eyes, but he does not yearn for her. Both Percy and Annabeth are still young, only twelve years old, and are more interested in surviving the quest than each other.
As for other female characters in the story, the one Percy yearns for the most is probably his mother; after she disappears in the golden cloud, Percy deduces that she has been taken by Hades and is willing to go to extreme lengths to rescue her. The reader knows that Percy's mom is fairly pretty, good-looking enough to tempt Poseidon, so she could be considered the 'beautiful woman that Percy yearns for.'
There is no specific person. It could be Percy's mother, Annabeth, or Aphrodite, as can be seen when they met in Titan's Curse.