The most significant moment between them is when Percy finally confesses his feelings for Annabeth, but they are interrupted by the arrival of Luke. They also share a moment of reassurance after they defeat Kronos and the war is over, but it's not a romantic one.
If you're looking for a more romantic moment between Percy and Annabeth, you'll have to look to later books in the series, particularly *The Heroes of Olympus* series, where their relationship develops further.