It's funny that you mention this actually, today I was watching Led Zeppelin's Celebration Day for the first time (very impressed I have to say) and my mum, who isn't much of a Zeppelin fan, was in the room with me for a few songs. To my surprise she thought No Quarter was really good, whereas (less surprisingly) she wasn't so keen on Dazed And Confused. I guess I have given some thought to a 'Led Zeppelin for people who hate Led Zeppelin' playlist - mainly consisting of thoughtful acoustic songs like That's The Way, ballads like The Rain Song or the mellow instrumentals Black Mountain Side and Bron-Yr-Aur.

If we put the boot on the other foot, my sister loves Taylor Swift and although I am not a fan I must admit there are certain songs of hers which I think are pretty good, mainly the more acoustic-type songs from the Red album (I can't stand the pop hits like We Are Never Getting Back Together etc, but the likes of Treacherous and All Too Well are good songs).

Still, hmm... an Eagles CD for people who don't like the Eagles? Bitter Creek and Journey of the Sorcerer are good ones to start with I think, the former is subtly dark and is all acoustic, which is rare, while JOTS is by their longest band instrumental. Here's a few suggestions of mine with a justification for each:
Get You In The Mood - Their earliest R&B song, and the only one (unless you count On The Border, which I think is a mix of rocker and R&B) performed by the original line up. It is less slick than a song like OOTN, as has been mentioned before it is vaguely similar in parts to certain bluesy Led Zeppelin songs.
I Wish You Peace - Not one of my favourites, but it's not quite like anything else they did during the 1970s - it's one of the few Eagles songs that I would say is neither rock or R&B, or country rock. I think of it as being their most pure M.O.R. song from the 1970s, it's not even really soft rock IMO.
Try And Love Again - The only 'optimistic' song on Hotel California, also the only one which I think truly has the quintessential California rock sound. I would say its appeal would be to people who dislike the more cynical approach of, say, LITFL, VOL or King Of Hollywood.
I Can't Tell You Why - Perhaps a slightly questionable inclusion, but not immediately recognisable as an Eagles song musically or vocally if the person isn't familiar with Poco or Tim's other Eagles songs.
The Greeks Don't Want No Freaks - Its clear humour value appeals to some, especially to those who dislike 'serious commentary' songs like LITFL or The Last Resort (I prefer Teenage Jail but I think it is less obvious that the song isn't meant to be taken too seriously).
I Dreamed There Was No War - Like JOTS, it is an instrumental. If the person is a fan of Dire Straits and/or Mark Knopfler, or dislikes Don or Glenn's voices, then they should hear this.