I would take East Lothian over Pebble any day
so many good choices, but I second East Lothian, if 'variety' and 'culture' count (the latter won't for some/many) - if the goal is a boys golf trip with the focus on 36-a-day and cards at night, it is very hard to beat Bandon...phenomenal golf and all right there - I love Bandon, but St. Andrews and East Lothian are tied for #1 in my book, assuming 'public' is defined as public-ACCESS, which virtually every course in Scotland offers the golfing tourist - frankly those spots may only be beat by suburban LONDON, where access to Sunningdale, Walton Heath, Swinley Forest, The Berkshire, Woking, Worplesdon, West Hill, etc etc etc is available to anyone with a sub-20 handicap and an email address...and the west end is a 30-minute train ride away!