I previously worked the North Tarrant county market prior to returning to Houston. Southlake and Westlake are highly desirable areas with very few affordable rentals. Rentals in these areas are highly desirable. I would suggest that you contact the Coldwell Banker or Keller Williams (Southlake offices) as they are larger offices with many local area listings and may be aware of "coming soon lease properties." I have run across condominiums in Colleyville in the $1,000 range but have rented properties in the area for as much as $5,000 per month.
Best of luck!