I can highly recommend Ilios, a 3-bedroom villa overlooking Hart Bay. The 1-week rate for 2 persons is about $2000 plus tax in off season (mid April to mid December), and double that in high season.
https://www.vrbo.com/464545Wife and I stayed there for 8 days in Nov 2014. Large private pool. Large master bedroom with balcony overlooking pool with views to Hart Bay and Caribbean. Master BR unit is separate from the living/dining room/kitchen unit. Short walk on a private trail to the rocky beach at Harts Bay. Less than 10 minute drive to Cruz Bay.
