The Chicago Manual of Style, 15th edition (2003) asserts this broad rule against combining question marks (or exclamation points) and commas (or periods):
6.123 When to omit comma or period. Neither a period (aside from an abbreviating period) nor a comma ever accompanies a question mark or an exclamation point. The latter two marks, being stronger, take precedence over the first two. ...
Chicago then offers two examples of this rule in action that are relevant to Araucaria's question:
"Have you read the platform?" asked Mark.
Her favorite songs are "Hello Dolly!" "Chicago," and "Come with Me."
I must say that I find the "Hello, Dolly!" example somewhat problematic. In that case we're dealing with song titles, and elsewhere Chicago specifies that song titles should appear in quotation marks—which conveniently frames each title in the series given above. (Inadvertently or not, Chicago omits the comma that is supposed to appear after Hello in the song title "Hello, Dolly.") But what if we were dealing with movie titles (which Chicago says should appear in italics)? Would Chicago insist on the following punctuation of a series of four movies?
Her favorite movies are What Did You Do in the War, Daddy? Hello, Dolly! Chicago, and Harold & Kumar Go to White Castle.
It seems to me that Chicago's blanket rule banning the commas after "Daddy?" and "Dolly!" in that list doesn't do readers any favors in this case.
Bryan Garner, Garner's Modern American Usage, second edition (2003) is less absolutist on this point than Chicago is:
A question mark follows every question for which an answer is expected. Typically, the next word begins with a capital letter. "He asked me, 'Why are you here?' A foolish question." But it's also possible to have a midsentence question mark—e.g.,: "Why should what is supposed to be a sacrament be performed with everyone looking on?—with that most desolating of all assemblages, a family reunion." Edmund Wilson, "Things I Consider Overrated" (1920), in From the Uncollected Edmund Wilson 127 (1995). Most authorities recommend not placing a comma after the question mark in such a sentence,; yet, though it seems a little old-fashioned, Wilson's em-dash after the question mark is quite acceptable.
In other words, the punctuation "everyone looking on?—with that" is quite acceptable, but the punctuation "everyone looking on?, with that" is widely objected to.
The Oxford Guide to Style (2002) doesn't directly address the question of adjacent question marks and commas, but it gives at least one example in which a comma is dropped from a sentence that might normally have had one if not for the presence of a question mark in the comma's expected place. The example occurs in a discussion of typical uses of question marks (section 5.8.1):
Where now? they wonder.
The focus of that example is the lowercase they (rather than uppercase They) following the question mark; but later in the same subsection, Oxford has this intriguing comment and example:
When the question is a single word in a sentence, there is normally no introductory comma, there may be no question mark, and the word may be italicized:
He wondered why.
The question is not whether but when.
The questions 'who?', 'what?', and 'where?' remain to be answered.
Clearly, as far as Oxford is concerned, the presence of a quotation mark after a question mark makes adding a comma after the quotation mark A-okay. This situation wouldn't arise under Chicago rules because Chicago follows general U.S. style in placing commas inside quotation marks instead of outside them.
I don't know whether Chicago would have favored using quotation marks or italics here to identify the questions as questions, but neither approach is especially attractive in the absence of commas:
The questions "who?" "what?" and "where?" remain to be answered.
The questions who? what? and where? remain to be answered.
If I were trying to punctuate the sentence while remaining obedient to the Chicaho guidelines, I would probably drop the quotation marks and the question marks and go with italics and commas:
The questions who, what, and where remain to be answered.
Back to Araucaria's example
Turning now to Araucaria's example—
You went there on Thursday? for instance, is not an interrogative clause but a declarative one, even if the utterance may be a question.
—it seems to me that relying on an italicized question mark on one side of "for instance" and a comma on the other to set that phrase off from the rest of the sentence is distracting, inelegant, and awkward looking. The suggestion by deadrat that Araucaria transpose the order of the question and the "for instance" neatly evades the issue:
For instance, You went there on Thursday? is not an interrogative clause but a declarative one, even if the utterance may be a question.
But what if Araucaria strongly prefers the original word order? In that case, it seems to me the only suitable evasion under Chicago's rules is to set off "for instance" with something stronger than commas. The logical options are parentheses:
You went there on Thursday? (for instance) is not an interrogative clause but a declarative one, even if the utterance may be a question.
You went there on Thursday?—for instance—is not an interrogative clause but a declarative one, even if the utterance may be a question.
Or you could rebel against Chicago and argue that the question mark is an integral element of the question block at the beginning of the example sentence and that it doesn't provide meaningful independent punctuation assistance to the rest of the sentence, including the would-be parenthetical phrase "for instance." If we start from that position that adding a comma after the monolithic question block simply brings the structure of the rest of the sentence more quickly into balance and coherence:
You went there on Thursday?, for instance, is not an interrogative clause but a declarative one, even if the utterance may be a question.
Chicago devotees (and others) may find the juxtaposition of question mark and comma unacceptably startling, but that punctuation has the great virtue of making clear immediately how the author is parsing his sentence—and the main purpose of punctuation, ultimately, is to promote clarity with regard to an author's intentions.