S on A is be no means overrated. The problem is that an awful lot of people visit it for the wrong reasons. If you find the Porter's jokes in the 'diversion' during the Scottish Play interesting and full of insight into the politics of the early reign of James I - S on A is going to thrill you, and it does thrill many, many visitors each year.
If, on the other hand, you prefer Indiana Jones to 'Two Gentlemen of Verona' you are probably going to enjoy Warwick Castle a whole lot more.
It's very expensive and I hate to see people shell out hard earned cash for stuff that they find boring.
If you're not that interested in Shakespeare there are better places to go and you'll find S on A 'Much Ado about Nothing'.
If you are a Shakespeare afficionardo it will be 'As You Like It'
N.B. It is my experience that Americans have a much greater knowledge of Shakespeare than most of the English.