Save/Help the Halflings! They offer rewards. Material and otherwise.
I know basilisks are immune to the gaze of other basilisks, but imagine if they weren't. Like the panda they would become ecologically unviable and endangered...
There are two large stones on the thinly wooded hillside above Tiringan. It is said that two basilisks surprised each other many years ago and fell in love at first sight. They also turned to stone at first sight. A local legend of star-crossed lizards: very moving.