To answer Chipoat's half-question, Machrihanish has no waiting list - you need two members to propose you for membership, but that's pretty easily done if you hang around the clubhouse for a couple of days - and dues are currently around £190/year, with a one-time £50 joining fee. It's also not at all difficult to get to Machrihanish if you're willing to pay for the (beautiful) 25-minute flight from Glasgow to Machrihanish. Hard to beat that, especially if the direct Newark-to-Glasgow flight on Continental is handy for you...
...of course, if you're just after the golf and not worried about the bonhomie of a golf club as such, there's always the season ticket at the St. Andrews Links Trust - unlimited play on 99 superb holes of golf, including the Old Course, for something in the neighborhood of £450/year (I don't know the actual price off the top of my head, but that's about right). And there's no waiting list or need to know any members - you just go to the Links Trust office, fill out a form and get your picture taken for an ID card, and you're all set!
Cheers,
Darren