What are the most beautiful public golf courses in the world?

I'd vote for Pebble Beach: history, pacific ocean, rotating US open site:

The Bay Harbor Golf Course, in Bay Harbor Michigan is beautiful!

Kingsbarns Golf Links...

If I may, Royal Cape Golf Club in Cape Town is pretty durn gorgeous. It's the oldest course in South Africa, dating back to 1885, and features some of the famous views of Cape Town. Cape Town gets rather windy, and it's a tough course, and the likes of Player, Els, Goosen, Oosthuizen, Schwarzel, and Sabbatini have all cut teeth here.

Private courses outside the US aren't as private as they are here, they have much more liberal visitor playing policies. You're restricted to certain times but you can basically call and reserve a tee time for these courses whereas in the US, it's very difficult unless you know someone to play say a Winged Foot. I played Bandon and walked PB and the weather sucks in the British Isles, but when it's good, the golf and views are amazing dare I say, better than what the US has to offer. Royal County Down (Northern Ireland) Ballybunion (Ireland) New South Wales (Australia)

The Old Course in St. Andrews.  Amazing in its design, detail and surroundings.  Most don't know its a public course and quite affordable.  The challenge is actually getting on (they have a lottery process).  The best time of year to visit is December where tourists and limited but the window to play is short since it gets dark early (I was the last one out on the course at 11AM).

The coastal holes at Bandon Dunes and Pacific Dunes are incredible visually and just as challenging because of their design and weather conditions.  I would argue the par-4 16th hole at Bandon Dunes is as pretty and fun of a hole anyone can play.

Old Head in Kinsale, Ireland merits inclusion in this conversation.  It is not my favorite golf course, but I have found the scenery to be second to none.

Mauna Kea, Big Island, Hawaii