Jazz for someone who doesn't like jazz.

n80

You’re going to get zillions of suggestions, any of which might or might not do much for you.

Unfortunately I find that Jazz is a gourmet dish (much like Classical). It demands certain conditions before it can be fully savoured, (for me a fast deep bass response and good timbral definition is a must). Otherwise,without those 2 key ingredients, it can like most gourmet food, often leave a disappointingly weak taste.

Pop music on the other hand is much like fast food - a dish that can be more or less enjoyed by anyone, anywhere.

Having said all that, my suggestion would be almost anything by Bill Evans.

If you stream, I suggest "The Jazz Groove" out of S.F. You will get a good selection of "laid back" Also Jazz24 out of Seattle will give you some good exposure. You might find some artists that you enjoy. Jazz is my favorite music idiom.

+1 on the Weather Report suggestion.
Also check out the live recording, "Swiss Movement", by Les  McCann with Eddie Harris.

It is really hard to guess what might click with any given listener.  I know someone who, when he was first interested in jazz, borrowed some CDs from me.  He liked Coltrane, so I put together a bunch of Coltrane CD's, and just for laughs, I threw in "Interstellar Space."  Guess which Coltrane CD he liked the most.

If you are looking for a survey, "The Best of Blue Note" is a decent double album to start off.  Blue Note put together better compilations in the past, but the current "Best of" is decent.

I would also get Sonny Rollins "Saxophone Colossus."  If the song "St.Thomas" doesn't hook you, I would be amazed.

george, as you will learn, jazz is a very broad and deep subject.  There are many periods, styles, and sub-sets.  So many that it can be difficult to make recommendations to anyone starting out.  Just look at the variety suggested here so far.

Two of the largest selling jazz albums of all times have been mentioned, Miles' "Kind of Blue" and Brubeck's "Time Out".  I think Brubeck is enjoyed by a broader selection of listeners and as such is more accessible.  Miles is deeper and may required more from the listener to appreciate.

Something like the Smithsonian album can be helpful since it presents a broad perspective time wise and with many styles.

Someone really basic would be Louis "Satchmo" Armstrong, AKA "pops".  He recorded from the late '20s to early '70s.  Here's one link to a classic performance with Jack Teagarden and All Stars -https://www.youtube.com/watch?v=gJFgKfuy1oM
 
Otherwise, I think a pop-oriented selection of jazz may provide one of the easier entries.  One subset is called light jazz.  It is quite popular but to me sounds like what I'd hear waiting in the dentist's office.  I think you can find some real jazz that is not heavy, jarring, or discordant that you can enjoy while offering more substance than the typical light jazz.  Here's the Ramsey Lewis Trio with a song very popular at the time -
https://www.youtube.com/watch?v=jsFST-7Hx-Y&list=RDjsFST-7Hx-Y&start_radio=1&t=3

Another of that type would be the Crusaders.  They started out as the Jazz Crusaders but changed their name in an attempt to appeal to a broader market (few jazz musicians sell albums or concerts in big numbers).  None the less, they were comprised by very good musicians -
https://www.youtube.com/watch?v=OahE2GGaGq4

Lastly to suggest one less pop-oriented example which is still melodic, try this by Bill Evans (the earlier pianist, not to be confused with the later sax player) https://www.youtube.com/watch?v=Nv2GgV34qIg

There is a wide, wonderful world out there in jazz, diverse enough that I believe most anyone can find something they like.  These are only a few suggestions.  Enjoy the hunt!