Did Tolkien ever state that The Hobbit was a children's book?

In fact, it wasn't just written for children in general - it was written for Tolkien's own children.

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Tolkien's own words:

The generally different tone and style of The Hobbit is due, in point of genesis, to it being taken by me as a matter from the great cycle susceptible of treatment as a ‘fairy-story’, for children.
- The Letters of JRR Tolkien, Letter #131

And:

The Hobbit was originally quite unconnected [to his Middle-earth legendarium], though it inevitably got drawn in to the circumference of the greater construction; and in the event modified it. It was unhappily really meant, as far as I was conscious, as a ‘children’s story’, and as I had not learned sense then, and my children were not quite old enough to correct me, it has some of the sillinesses of manner caught unthinkingly from the kind of stuff I had had served to me, as Chaucer may catch a minstrel tag. I deeply regret them. So do intelligent children.
- The Letters of JRR Tolkien, Letter #163

And:

When I published The Hobbit – hurriedly and without due consideration – I was still influenced by the convention that ‘fairy-stories’ are naturally directed to children (with or without the silly added waggery ‘from seven to seventy’). And I had children of my own.
- The Letters of JRR Tolkien, Letter #215

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The Tolkien Society's words:

The Hobbit was originally a story Tolkien told to his children. In this form it was composed sometime between 1929 and 1936.

It was published in 1937.

It is described as a fantasy novel, a story of heroic quest, and a children's story.
- Tolkien Society's The Hobbit: An Introduction