This is from an article about setting goals: 'We need to ask ourselves what is it that we want in order to feel truly accomplished.'
Compared with 'We need to ask ourselves what it is that we want in order to feel truly accomplished', which sentence sounds more natural? Are they both grammatically correct?
Depending on how you punctuate the sentence, you can use either of the wordings you suggest:
We need to ask ourselves, what is it that we want in order to feel truly accomplished?
or:
We need to ask ourselves what it is that we want in order to feel truly accomplished.
Since the punctuation you give does not treat the wording after ourselves as a direct question, the "what it is" form is appropriate. This is the essence of sooeithdk's comment above.
But beyond that, the second sentence has an ambiguity problem: It is possible to understand the phrase "in order to feel truly accomplished" as modifying either "we need to ask ourselves" or "what it is that we want." The superfluous phrase "it is that" makes this ambiguity a bit harder to see, so let's remove it from the second sentence:
We need to ask ourselves what we want in order to feel truly accomplished.
On the face of it—unless we take the absence of a comma after want as proof positive to the contrary—this sentence can be understood as saying that we can feel truly accomplished simply by asking ourselves a particular question (namely, "what do we want?") Or it can be understood as saying that we need to ask ourselves a particular question (namely, "what do we want in order to feel truly accomplished?"). The second interpretation is far likelier to be correct than the first, but the author could have avoided all ambiguity by framing the statement in simpler terms:
We need to ask ourselves what would make us feel truly accomplished.
Interestingly, this sentence could be punctuated as a direct question without any change in word order:
We need to ask ourselves, what would make us feel truly accomplished?
Both the declarative and interrogative forms of this sentence are correct as given.
In your indirect quotation,
"ask ourselves what it is that we want..."
is good grammatically.
However, if it were a direct quotation, it would need inversion and an actual question mark
