As far as accessibility goes I seriously doubt that there is a poster on this site that can name 10 courses in the United States that they want to play and can not. As a matter of fact most private clubs "advertise" on their web sites that they want you to come and play. My God, the foundation of this web site is based on this very access.
I have next to no connections even though I belong to a small club just outside Philadelphia, but I could probably come up with 20 courses I want to play and cannot:
Augusta National
Cypress Point
Sand Hills
Merion East
Pine Valley
National
Camargo
Seminole
Applebrook
Gulph Mills
Shinnecock
Sebonack
Chicago Golf Club
Brookline
Riviera
Valley Club at Montecito
Oakmont
Winged Foot
Scioto
Butler National
Mind you, I've never contacted any of these courses and asked if I could play a round, but I'd say accessibility in the UK is definitely more open than here.