Hands down the best burger is the one I grill, and I will put my recipe below, but second best and number one for these purposes is the AAFES burger circa 1985 Okinawa, Japan. As far as I know the AAFES burger was unique to the exhange system on Okinawa. I have looked at other locations and while they may have have an "AAFES burger" it wasn't the same. The AAFES burger was a pretty big burger probably 1/3 to 1/2 pound before cooking and the meat had kind of a unique flavor, like they seasoned it with just a little soy and teriyaki, just a hint of salty sweetness. The meat also grilled incredibly well. I grew up in a time and place where hamburgers were cooked very well done, and that meant a crust on the meat that was crunchy when you bit it. (Alton Brown will tell you that meat should never be cooked past medium rare. He is WRONG). The AAFES burger had that texture, but the inside was still juicy. Not red, just juicy. The bun was toasted and the burger was dressed with "AAFES sauce" which was their version of McDonald's secret sauce. I believe it was Thousand Island with a little soy sauce mixed in but I can't say for sure. It was insanely good. The standard vegetation finished it off. My mouth is watering and I am having Okinawa flashbacks as I type.
Unfortunately the fries weren't as good - Best fries, Peggy's Restaurant Pohang, and Uncheon Korea (she would pack up and follow the troops) I can't even say why they were so good because as I think back on them objectively they should have been bad. I think it must have been the huge quantities of OB beer, Soju and whatever that local spiced rum was, that we were consuming.
As promised, my burger recipe:
1 to 1 1/2 pds 80/20 ground beef
1/3 cup Yari Teri Teriyaki
1/4 Worcestershire sauce
1/4 cup dried minced onions
1 cap liquid smoke
Salt and pepper the living hell out of the beef. Let it sit for 30 minutes plus. Add the other ingredients. Let it sit for at least an hour. It has to sit to let all the flavors meld. Make 4 patties. Get the grill as hot as humanly possible, Mine only goes to 800 so if you can get it that high you should be good. Grill the patties for 2 minutes on one side, flip and two minutes on the other. Turn the heat down so that it is about 500 degrees and cook for 4 1/2 minutes more on each side. Toast the buns and serve.