In its review on January 12, 1959, Time magazine called this album, "An infectious musical dialogue between two of the sassiest fancy talkers in the business. C. & C. give slick and witty readings to a selection of retreads — 'On a Slow Boat to China', 'You Came a Long Way from St. Louis' — and introduce a punchy, potential hit named 'Calcutta'. One of the most intriguing vocal entertainments since Noel Coward had his famous chat with Mary Martin."
Variety said, "Two savvy singers team up in a charming rundown of a dozen numbers for a pop set with adult appeal." 
Billboard also liked it, saying: "A lot of charm here — A flock of tunes carrying different place names, carrying out the idea of the album title... Cover also carries out the theme. Performances are very smart, with occasional interpolations and asides by Crosby and Clooney. Arranged and conducted in grand style by Billy May."
The British publication The Gramophone in their April 1959 edition went further. "Even so for the duet-warbling of the month I would turn to RCA SF5022 (Mono RD27105): 'Fancy Meeting You Here' with Rosemary Clooney and the old groaner himself, Bing Crosby, bumping amicably into each other in a dozen stage sets scattered around the world...The Billy May accompaniments throughout are first class, and so, obviously, is the singing; but principally it is the infectious easygoing good humor of the record which remains in the mind. That, and an occasional twist of lyric; no record can be neglected which ends a nostalgic and twang-ridden version of the 'Isle of Capri' with 'I've often felt that we both might have stayed there, if it weren't for those stale mandolins.'"