Looked into this when I thought I was moving to Katy. (Last year some time) Junior Membership was $1500 - $3000 initiation and dues were $300 per month plus some minimum monthly spend. They seemed pretty desperate for members as they discounted the initiation immediately from 3000 to 1500 and offered to roll it into my first year's dues.
The course was nothing spectacular, but I always enjoy playing/hanging out there.