The quote's attribution to St. Augustine is indeed widespread, judging by the dozens of images featuring the quote:
To fall in love with God is the greatest romance;
to seek Him the greatest adventure;
to find him the greatest human achievement
The sleuthing effort has been done already and documented at the Fauxtations blog, making the case that the quote does NOT belong to St. Augustine:
... it’s Fr. Raphael Simon, O.C.S.O., who is credited with it as far back as a 1964 story in Newsweek. I can find something like it in Fr. Simon’s book Formation of the Priest, on p. 125:
Now to fall in love with Jesus requires faith. We have to know the story of Jesus, of His coming into the world, of His teaching and deeds and fellowship in this world, of His passing to the Father, of His coming back in life after death to talk with His disciples and continue His fellowship with them, of His going to the Father and sending into our hearts the Holy Spirit and His love. This is the greatest story in the world, the greatest romance, and we are called to the greatest adventure.
Obviously that’s missing the “human achievement” part, but it shows at the very least that Fr. Simon wrote something along the lines of the quotation, and I suspect he was quoting himself here, in modified form (or perhaps he later expanded on this thought).
I don’t know who attached it to St. Augustine; the earliest I can find it attached to his name is in 1984, in How to Live Life to the Fullest: A Handbook for Seasoned Citizens.