If you're one of those people who DO NOT like musicals (also, how did you get here??) and you're too smartsy-fartsy for traditional stuff, if you want something that will make you think and not get annoying, I'd say Assassins is a good place to start.
Also -- even though the original cast is fantastic -- go with the revival starring Neil Patrick Harris, because it has more (more everything: songs, monologues, scenes, etc etc).
This advice also applies to anyone who doesn't like Stephen Sondheim (and he's my hero so stop talking to me until you come to your senses).
First, this musical is basically perfect. I mean, MY GOD. How are we even going on our day to day lives?? It makes you think about your own life, it makes you think about the populous, it makes you think about mental illness, depression, cults, the "American Dream"... it makes you think about the media, history and why some names are remembered and others are not... it makes you think a LOT, OK??
Second, Assassins features what I consider a legitimate POP SONG ("Unworthy of Your Love"), sung by two insane people, completely beautifully, passionately and seriously. WHAT MORE DO YOU WANT????
Third, again, this is Stephen Sondheim, so it's hard to go wrong. The music is complex and meaningful, yet somehow peppy and bright. There is a surprising amount of joy for subject matter so dark, sung by a bunch of characters that killed (or tried to kill) people.
Music and Lyrics by Stephen Sondheim
Book by John Weidman