It is too easy to just pick two ideal courses very close to each other that we would all love to play.
How about making this challenge more interesting?
What if you have $1000 to spend (an unexpected windfall/bonus), and are given one day for guilt free all golf (no house chores, no family obligations). And you have no imaginary access to the great private courses. So either play a public or resort; or play a private you have realistic access to get on.
One day is not enough to fly from my New England home to go play golf for a day across country or in another country.
So what great 36 would I select within a couple hours of my home in Springfield MA to make a great one day golf outing.
Some immediate possibilities:
Taconic (at Williams College) followed by the 9-hole Hotchkiss.
Tripp Memorial in the morning; lunch at an Irish pub in Dorchester; followed by George Wright in the afternoon; and then finished off with watching 9 innings at Fenway in the evening - in the bleachers. A great common man's day of golf & baseball.
I possibly could pull off a 36-hole day at two great privates both within 30 minutes of my home - The Orchards in the morning; lunch in Northampton; then Longmeadow C.C. in the afternoon.
If I drive down to LI the night before, another great 36-hole day would be Bethpage, with 18 on The Black course & 18 on The Red course. (A lunch of a hamburger in the clubhouse is enough for me if I can play these two grets in one day.)
In my hometown of St. Louis I can think of two interesting public options:
One would be 18 at Forest Park; lunch at one of the great Italian restaurants on The Hill; then 18 at Normandie.
Second option, 18 at Gateway National, then 18 at Annbriar (no real good lunch options come to mind).
When I used to work at Algonquin Golf Club and we could play on Monday afternoons, we used to do a day like this. It would start with an early breakfast at Perkins, then 18 at a public course somewhere in the St. Louis area, then lunch at Steak N Shake, then 18 at Algonquin. Life was perfect then.