UK companies
Doris,
did you check out the UK travel companies that specialise in this ? They advertise in the magazines - I think one is called Ranch America and there is at least one more.
You might not end up choosing to use them, but it is useful research so you can be sure what kind of holiday you want - lessons, working ranch etc etc
Also if you can find a copy of an american horse magazine anywhere, they have a lot of ads in.
This does not get the personal 'recommendation' you asked for, but you may want something different to me !
I did a holiday about 10 years ago where I was lucky enough to spend a week with Lynn Palm in Michegan, and then I spent a week in Arizona. Lynn Palm is a top trainer so I felt very priviledged - a friend who breeds Quarter Horse in the Uk arranged it. The week in Arizona was much more low key (and warmer - it was in Feb so Michegan was snowy !).
Don't forget to think about the time of the year and location. The guys in Arizona told me they shut down in May 'cos it was just too hot !