Translation of 'I do not need what I think I need'
First,


  我不需要我认为我需要的东西 


Is okay.

Next:


  Is 的东西 necessary or is 我不需要我认为我需要 sufficient to convey the meaning?


If anything 东西 is unnecessary. 的 on the other hand is essential.

的 has the function to turn verbs into nouns.

需要 means “to need,” 的 turns to need (需要) into 需要的 and means into something more like - what (I) need -or- the things (I) need.

So 我不需要我认为我需要的东西 could be better phrased as 我不需要我认为我需要的.

It might be more natural to put it in a flipped order though (i.e.: what I think I need - I don’t (actually) need).