The NOAD (New Oxford American Dictionary) has a note about using any:
When used as a pronoun, any can be used with either a singular or a plural verb, depending on the context: "we needed more sugar but there wasn't any left" (singular verb) or "are any of the new videos available?" (plural verb).
In "English Grammar" (David Daniels & Barbara Daniels, ISBN 0-06-467109-7), any is listed between the pronouns that can be either plural or singular, among all, more, and some.
Looking for "do you have any idea for" on the Corpus of the Contemporary American English, I get a single sentence.
But what happened was that the network came to us—because we have a little production company that does my specials—and said, do you have any idea for a show?
Looking for "do you have any ideas for," I get three sentences:
Do you have any ideas for the next movie?
Well, then," said Avette, "do you have any ideas for another topic?"
Do you have any ideas for me?
Looking for "do you have any idea(s) to," I get the following sentences:
Do you have any idea to this day how you stacked up against the men?
So, do you have any ideas to help cows and sheep stop with the gas problem?
Do you have any ideas to boost union membership?
As side note, the Corpus of Contemporary American English doesn't have any example of the phrases I searched for the period 2010-2012. The sentences containing "any ideas to/for" are dated 2005-2009 (the most recent ones), while the sentences containing "any idea to/for" are dated 1995-1999.