Nathan has been engaged to Miss Adelaide (Vivian Blaine) for 14 years, but has no interest in marriage, "old ball and chain." Sky is not interested in women at all.
Especially when the girl turns out to be the prim-and-proper Sergeant Sarah Brown (Jean Simmons) of the Save-a-Soul Mission (a take on the Salvation Army).
Sky knows his way around a bet; he tells Sarah that he will fill her mission with sinners in exchange for the dinner. She agrees, and naturally they fall in love -- you can't have everything.
There is also a group of gamblers led by the corpulent Nicely-Nicely (Stubby Kaye), who display no heterosexual interest.
No beefcake, but the period costumes are great. So are the songs.
The stage version is even less hetero-romance-bound. Nathan Detroits have been played by Robert Guillaume, Bob Hoskins, Nathan Lane, and Oliver Platt, and Sky Masterson by Robert Alda, Peter Gallagher, Ewan McGregor, and Craig Bierko.