If you want to avoid the Nimzo, 3.Nf3 is the main way to do it. However, Black then has a choice of:
The Queen's Indian (3...b6)
The Queen's Gambit Declined (3...d5 4.Bg5)
The Ragozin Defense (3...d5 4.Nc3 and now 4...Bb4 instead of 4...Be7), as played
Your other option is to go for the Catalan with 3.g3.
If you don't want to play the Catalan, I suggest looking at games of top players in the Ragozin, especially Arkadiy Naiditsch.
I'm happy playing 4. Nbd2 against the Bogo, it's the delayed 3. ...d5 that had me scratching my head for a plan. I might try 4. Bg5 and see how that goes for a bit.
Thanks for the advice! 
A quote keeps getting stuck in my head:
"If you avoid critical lines, you avoid learning anything about chess." 
Instead of avoiding it, learn it.
Andre_Harding pretty much sums it up, along with paulgottlieb & DrSpudnik
So, what's the problem with playing the White side of the NID? Playing 3.Nf3 here is making life very easy for Black, just like it does in the QGD because you are not hammering away at d5 - like you're supposed to IMHO. There must be some variation in the NID that will suit your style: Classical 4.Qc2, Spielmann 4.Qb3, Rubinstein 4.e3, Saemisch 4.a3 or something else.
Recently drew against very strong competition, apparently all book moves until Move 16. I wanted to avoid Nimzo-Indian by playing 3. Nf3 but I'm not too familiar with K-side fianchetto games and ended up with a Nimzo-ish game. Any suggestions/examples for continuations other than 4. g3 after 3. ...d5 are much appreciated.