I have had the good fortune to play many of the aforementioned 36-hole combinations, and would not want to pick a single favorite. However, maybe the best weekend I've ever done was on behalf of two of my interns -- pardon if I've told this story once before, but it's not on this thread.
When we were building the North course at Stonewall, I told my two interns (Kyle Franz and Philippe Binette) that I would take them up to Long Island for the weekend and show them some golf. I had only arranged to play 18 holes -- the point was to let them walk and see the courses. But we did all bring our clubs.
We started at Garden City first thing Saturday morning, pulling into the maintenance building. I'd intended to walk the course, but the superintendent INSISTED we play ... he was about to get fired and knew it might be controversial to send three visitors off #10, but he didn't care at that point. So, the boys got to play Garden City.
When we were done we drove out to Friar's Head so we could walk it. Jim Kidd was still the pro, and I didn't want to ask him to play because I knew he could get in trouble for sending us out without a member. But it was raining by then and there were no members out, so he invited us to play if we wanted -- so we played 18 holes in the rain there, too. Pretty good double, GCGC and Friar's Head.
Next morning, we are on the tee at Shinnecock, to play our one scheduled round, with a member friend of mine. The boys thought that was the best course they had ever played, so, I told them we'd go look at one other -- National. I go into the pro shop and ask if we can walk the course -- fine. And then when we're on the second fairway, the caddiemaster comes out and invites us to play, as long as we'll take caddies. He had a couple of guys who hadn't got loops and it was the end of the day.
I don't know what my best 36-hole day is, but I'm pretty sure I know what are Kyle and Philippe's.