Along the way, he discovered that some of the layouts had been forgotten or rendered irrelevant, that one Open venue had vanished, that another had been abandoned and its name affixed to an adjacent 18, and that some of America's best-known courses - such as Oakmont, Winged Foot, and Merion - earned their reputations.
"Merion is one of my favorites," Hines said during an interview the week before the 2013 Open was played there. "Every architect should have to go play there before they're allowed to build a course. It's just got everything you need."
Hines, 54, the professional at Cape Fear Country Club in Wilmington, N.C., unknowingly began his endeavor in 1981. After graduating from East Carolina, where he captained the golf team, he had taken a job at Northwood Club in Dallas, site of the 1952 Open.
"I got an immediate sense that there was a very different flavor between your normal golf courses and your U.S. Open courses," he said.
Later, with some Northwood members, Hines went on a golf excursion to the Northeast, where the group played Merion, Aronimink, the National Golf Links, Shinnecock Hills, and Baltusrol.
"So you play those five and it's like, 'How does it get any better than this?' " he said.
That trip was so successful that they made an Ohio-Western Pennsylvania swing to Canterbury, Inverness, Muirfield, Firestone, and Oakmont.
"At that point, we were still going more for the big-name courses," Hines said. "But after three or four of those trips, a friend said, 'You know you've played an awful lot of U.S. Open courses.' That interested me.
"I started researching. I found out there were 49 of them - actually 50, but Englewood in New Jersey had closed. So I started nibbling away."
Once he gave up his dream of playing on the PGA Tour - he failed to earn a card at qualifying school on several occasions - the pace of his quest quickened.
He played Open venues in bunches with friends, then began to pick them off one-by-one on his own. As difficult as the golf was at many of those exclusive venues, securing tee times was even tougher.
"They all had their rules, and you had to respect them," he said. "It wasn't easy getting on at Baltusrol or Riviera. Chicago Golf Club was brutal. Sometimes they paired you with a member. Sometimes you had to beg, borrow, and cry."
Merion was easy, since one of the Northwood golfers was also a member there.
Hines shot good rounds - a 65 at Northwood and a 70 at Medinah when it was set up for an Open - and bad.
"Oakmont and Winged Foot beat me up the worst," he said. "Bethpage Black, it's such a long course to walk that you're beat up by the time you finish a six-hour round there.
"And Merion. I've come across that road [Ardmore Avenue] five times and I've been at even, 1 under, 1 over. But I think the lowest I ever shot there was a 77. Fifteen, 16, 17, 18 have just eaten my lunch every single time."
Some of the courses, particularly those that haven't hosted an Open since the event's early days, were pleasant surprises.
He liked Philadelphia Country Club (1939) much better than the Philadelphia Cricket Club (1907, 1910). Among the other out-of-the-rotation "sleepers" Hines enjoyed were Myopia Hunt near Boston, the site of four Opens from 1898 to 1908; and three Chicago-area courses, Chicago Golf Club, Onwentsia, and Glen View.
"Chicago Golf Club is like Merion," Hines said. "If somebody gave you a million dollars and told you to improve it, you'd go crazy because it's already perfect."
Englewood (N.J.) Golf Club, where the 1909 Open took place, is the only U.S. Open site to have disappeared, replaced in the 1960s by a ramp to the George Washington Bridge.
The Country Club of Buffalo's name still exists, but it's not the course where Philadelphian Johnny McDermott won a second consecutive Open in 1912. That's now a 5,700-yard municipal track called the Grover Cleveland Golf Course.
Though the Open wasn't held during World War II, the U.S. Golf Association teamed with the PGA of America to sponsor a national event in 1942, the Hale America Open, at Ridgemoor Country Club outside Chicago. Ben Hogan won it, and Hines figured he'd better play the course in case someone someday decided to reclassify it as an Open.
Playing them all
His Open puzzle completed in 2011, Hines has since turned his attention toward any course that has hosted a major championship.
"That's my next goal - playing all of them," he said. "I've played most of the British Open courses, but I need one more trip to play the English courses. I've played Augusta. I've still got about 30 PGA courses left [including Llanerch Country Club in Havertown].
Unlike the Open courses, which tend to be clustered on the two coasts and in or near large Midwestern cities, the PGA venues are spread out across America.
"But the good Lord and my body willing," Hines said, "I'm going to play them all."
Perhaps Hines' most prized possession from his Open journey is a photo of him firing a shot from the exact spot in Merion's 18th fairway where Hogan hit his famous 1-iron in 1950.
It hangs in his office next to Hy Peskin's iconic Hogan photo, which is signed by the legendary golfer.
"I hit 3-iron from there," recalled Hines, who idolized Hogan, "and landed 10 yards short. It ended up 15 yards over the green, and I was dead coming down that hill. I couldn't stop it on the green."
The experience gave him a sense of what the baffled golfers in the 2013 Open went through there.
"That's one tough hole," Hines said, "and one great course."
Contact Frank Fitzpatrick at 215-854-5068 or email@example.com. Follow @philafitz on Twitter. Read his blog, Giving 'Em Fitz, at www.philly.com/fitz