When I played the Nimzo/Queens Indian I played the Sicilian Kan versus 1.e4.  This enabled me to reach a lot of Hedgehog type positions.

I got this idea from Jon Edwards book the Chess Analyst

Taimanov was a Nimzo addict and he played... well, he played the Taimanov Sicilian!   He also played the French occassionally.  Spassky was a Nimzo player who was pretty much universal.  However Spassky is probably best known as a Spanish (Ruy Lopez to us Yanks) player.

I think there are a couple of natural fits with the Nimzo against 1.e4.  The first that comes to my mind is the Alekhin.  They are both Hypermodern defenses that encourage White to overreach.

Another good idea, backed by Taimanov, Najdorf and many others, is to play the Sicilian.  The Nimzo and Sicilian (probably Boleslavsky/Sveshnikov types of games) share the following:  they both reward research; they are both more counter-attacks than actual defenses; and they are both fundamentally sound.   

When you see a list of great players who played the Nimzo, it's almost like reading off a list of Sicilian variations.  There's probably a reason for it.  But having said that, 1...e5 played classically also makes sense.  So, there you have three first moves as Black and you're probably just as confused as ever!  I aim to please!

Not a nimzo addict either but will play it on occassions. But  most of the time will play the najdorf against e4. Occasionally will try out the Alekhine's with a KB fianchetto. It resembles a KID in some ways or other. -  K-side fianchetto & playing against broad pawn ctr.

I am very curious to hear from chess players who are Nimzoindian addicts, what they play against e4?
Or from experts, what they consider would fit from the point of style to somebody who likes the Nimzoindian against d4?