Thanks for your suggestions.
All the hotel you mentioned seems very good as CAT 4.

In USA, what do you think of Westin Kierland in Arizona ?
In winter, the hotel is quite expensive but still same CAT 4 .
I plan to go to Las Vegas in Jan, too, so I might visit Kierland for golfing.
Is it cold to play golf in Jan?

Turnbury sounds nice and I really wanted to go there for golfing, however, I was watching British Open and it looked cold in June/July. Is it playable in March at Turnbury?

I am from Hawaii so I don't care the strong wind, but I care the cold weather when we play golf.

Thanks again!