Strangelove is one of my favourite films ever, but I think you need to be in the right mind to appreciate it. I first saw it many years ago, and I understood the humour but didn't laugh out loud the way I do now. Clockwork and Shining are obviously more visual pieces, but Strangelove has the tightest script out of all the Kubrick I've seen. That, coupled with the great use of monochrome that you mentioned, is the tipping point for me.
You mentioned the visuals of Clockwork, and while they certainly were put to good use in that film, I got the feeling that there was nothing BUT visuals in Eyes Wide Shut. It was beautiful to look at, but didn't seem to offer anything more. (I blame Tom Cruise mainly; he seemed to have the same expression on his face the entire time, even when it was covered by a mask!) Maybe it's just me, though.
This has already gone on waaaaay too long, but Strangelove's my fave by a country mile. Then Shining, then Clockwork (of which I really love Malcolm McDowell - probs my fave performance in a Kubrick film), then 2001, then Eyes Wide Shut, then Lolita which I actively dislike.