When do Harry and Hagrid go to Diagon Alley for the first time what is date?

While the specific date isn't stated in the book, Harry and Hagrid's first trip to Diagon Alley takes place shortly after Harry's eleventh birthday.

Here's the timeline:

* July 31st: Harry turns eleven.

* Later that day: Hagrid arrives at the Dursleys' and reveals Harry's magical heritage.

* The next day or two: Harry and Hagrid travel to Diagon Alley.

Therefore, we can safely assume their trip to Diagon Alley occurs sometime between July 31st and August 2nd, although the exact day remains unspecified.