The word however is not inherently ungrammatical at any specific point in a sentence (beginning, middle, or end, for example); its grammaticality depends on the context in which it appears.
Nevertheless, as a matter of style, many commentators have criticized the practice of beginning a sentence with however. Bryan Garner, Garner's Modern American Usage, second edition (2003), addresses this issue:
however. A. Beginning Sentences with. It seems everyone has heard that sentences should not begin with this word—not, that is, when a contrast is intended. But doing so isn't a grammatical error; it's merely a stylistic lapse, the word But ordinarily being much preferable. [Internal cross reference omitted.] The reason is that However—three syllables followed by a comma—is a ponderous way of introducing a contrast, and it leads to unemphatic sentences.
In part B of his discussion, Garner argues that however naturally emphasizes the word immediately preceding it in a sentence—and this leads him to consider the merits of putting however at or near the end of a sentence:
C. Undue Delay in the Sentence. Because of the point established in (B), it's quite unwise to put the however very far into a long sentence. The cure is an initial But—e.g.: "We use data only for individuals from the former West Germany in this study, however, and restrict our attention to data reported for the years prior to 1989, the year of reunification."
But again, this is all style advice, not grammatical analysis. The sentence you give as an example—
I don't think it'll be useful, however.
—is short, and your positioning of however in it emphasizes the appropriate word (useful). Under the circumstances, I don't think it is any less effective than saying
But I don't think it'll be useful.
and I certainly don't see any reason (other than personal stylistic preference) to reject it in favor of
I don't think it'll be useful, though.