Harry runs into his Gryffindor roommates, Seamus Finnigan and Dean Thomas, as they are shopping for their school things before the 1993-1994 school year in Diagon Alley. They were looking at the newly released Firebolt broom on display in Quality Quidditch Supplies (PA4).
From the text, it's clear that Harry met Seamus and Dean several days before finally meeting Ron and Hermione on the 31st. We'll place the date as the 25th, but the range could be anywhere from August 16, when the Firebolt is displayed in the shop window, to August 30, the day before Ron and Hermione arrive.
As the days slipped by, Harry started looking wherever he went for a sign of Ron or Hermione. Plenty of Hogwarts students were arriving in Diagon Alley now, with the start of term so near. Harry met Seamus Finnigan and Dean Thomas, his fellow Gryffindors, in Quality Quidditch Supplies, where they too were ogling the Firebolt; he also ran into the real Neville Longbottom, a round-faced, forgetful boy, outside Flourish and Blotts. Harry didn't stop to chat; Neville appeared to have mislaid his booklist and was being told off by his very formidable-looking grandmother (PS4).
From the Web
Harry Potter Wiki: Quality Quidditch Supplies
Tags: brooms / broomsticks Diagon Alley businesses meetings racing brooms shopping