Before I joined the club I used to do this pretty much every year at Elie. Buy a 7 day pass, play every morning at the crack of dawn on my own, then a few times during the week again in the afternoon with members.
If I had to pick 10 (and not picking anywhere I'm a member of) it might be these:
Ganton - great choice this, quiet, welcoming and a short walk from the Greyhound. Only issue might be the lack of things to do in the evenings.
Kington - these courses have to be fun and there has to be a chance they'll play differently from day to day. Kington ticks both.
Barnbougle Dunes/Lost Farm - I can't imagine staying at Barnbougle and not playing both courses but if I could only play one I'd be happy with either. Worth it just for the views.
Prestwick - a fabulous suggestion from Ally. I'd need to be with a group so that at least some of the golf was foursomes.
Yale - great fun, again, and this stay would be long enough to work out how to play some of those holes.
Swinley Forest - not the best of the heathlands but a course that would repay the repeated plays and a great club to be around for 5 days.
De Pan - this strikes me as a great place to hang around for 5 days, the course is a delight and Utrecht is a city I'd love to see more of.
Kingston Heath - I played so badly there on my one visit but a fabulous course and welcoming club. I struggled to decide between KH and RMW but, for the sake of this exercise (and limiting myself to one course in Melbourne), KH wins this time.
New South Wales - 5 days in Sydney? Walking over the hill on the 5th 8 times in that period? A chance to settle in and enjoy the club's wine cellar (I'm assuming that's OK)? A chance to marvel again at the mess Greg Norman created at the 18th? It's a shoe in.
RCP - again, I'd need company to play some foursomes, but great fun (again), different challenges from day to day and a fabulously welcoming club.
What strikes me is that I considered a couple of my favourite courses (Muirfield, Silloth) and dismissed them (too hard for 8 games in 5 days, not enough to do in the village) but see that The Yank did choose Muirfield!