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

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. 

Yeah, numerous Mose Allison comments, he was a gem... moody, quirky sprinkled with humour throughout

The Mose Chronicles v2 in London* is not to be misses 

Yes I can understand you ,years ago ,I worked 11 pm to 8 am at the old PO.and the guy at the desk would play Free Form Jazz....I hated it...just blasting  note without any form of music ,Terrible....But you need other stuff... Older jazz Like  Chat Baker,Gerry Mulligan,The Rippingtons.Thats a good start, it's music,with form,classic songs....Enjoy my  Man and  have a Great Christmas....