Can you recommend Jazz for some one that doesn't like Jazz?

Jeff Beck - Wired or Blow By Blow

As an old rocker myself I recommend:

Archie Shepp

Return to Forever / "Romantic Warrior"

Clarke, DiMeola, Ponty / "Rite of Strings"

Madeleine Peyroux

Mahavishnu Orchestra - fusion

Vince Guaraldi / "Oaxaca"

Isao Suzuki / "Blow Up" (preferably on 45rpm vinyl)

Patricia Barber

Brian Bromberg / "Brombo!"

Linda Ronstadt / "What's New" "Lush Life" etc

Chris Botti / "To Love Again - The Duets"

Passport / "Hand Made" "Cross-Collateral" "Infinity Machine" - fusion

Pierre Moerlen's Gong - All are good to great - fusion

John Whitney / "Classical Jazz"

Lenny White / "Venusian Summer" - fusion

Melody Gardot

Ponta Box / "Modern Juzz"

I would also look at some of the various samplers to get an idea of the artists you prefer. Some that come to mind are from Marantz, Burmester, Vevus Records

Watch the Ken Burns series, "Jazz" on PBS.  That may go a long way in clarifying your understanding of jazz.  My mom took me to hear Armstrong when I was 10 (1952), and he sold me on jazz immediately.  The Hot 5 and Hot 7 records virtually defined the direction of jazz (and, to a degree, pop and rock, and even Broadway) for decades.  Listen to those recordings a number of times, and pick out a different instrument to follow each time you listen.  Finally, take in the numbers as a whole.  Armstrong said they did not improvise--everything they did was planned--variations on themes,  Also, pick up the Willie Humphrey performance of "My Blue Heaven" on YouTube.  His extended clarinet solo there is a model of elegance.  For utter abandon, find the YouTube recording, "Ice Cream," by the December Band in 1965.  John Handy's extended sax solo in the middle of the piece will have you shaking your head just as a few members of the band were doing.  Finally, pick up a few of Tuba Skinny's long sessions on YouTube, and if you get a chance, hear them live.  Their vocalist, Erika Lewis, will  make you cry. They are preserving traditional jazz as well as any group in the world.   

Wow. If I were a guy who didn't know much about jazz and I asked that original question these responses, put together, would have left my head spinning!  Humor aside, if you like Mose Allison, you're pretty much already there.  

Maybe start by process of elimination, or simplify your selection process.  Given the wide range of musical styles referred to as JAZZ, start by identifying what appeals to you musically then choose artists that fit. For me, not really into big band, Dixieland, fusion, or experimental styles.  Jazz guitar, piano, saxophone, female vocals in smaller groups or ensembles are more my style.  Maybe call it more ‘traditional’ jazz.  Several artists listed in this thread fill my somewhat limited collection, meet my criteria, and I really enjoy during repeat sessions.  FWIW, several have passed but left prodigious musical  legacies.  The musical prowess and technical proficiency of the greats make most rock musicians sound like amateurs by comparison, IMHO.