I live smack in the middle of La Cantera and Hyatt Hill Country and personally like them almost equally. Normally not as many people at the Hyatt course in my experience. Also have an extra 9 they typically let you play for the price of 18. Only difference I have found is Hyatt charges out the rear for beverages on course (alcohol). If you have never played the La Cantera Palmer Course it's an absolute must simply because of the terrain and views.
It's been a while since I played La Canterra and I still preferred Hyatt for the price and availability. Cedar Creek is a nice muni that is close, it runs hot and cold, in good condition right now but plays slow at times.
My son and I played Hyatt Hill Country this weekend, and even with all the rain, we really enjoyed it. I've always loved the course, and think you'll enjoy it.
La Cantera Resort is my favorite followed by Hyatt followed by LC Palmer. To the point above, Palmer is good if you really value the scenery and uniqueness factor, but as far as actual golf, it's too tricked up for my liking.