He does his homework out in the open, eats free ice creams, picks up his books, and repeatedly stops by Quality Quidditch Supplies to admire the Firebolt. (PA3)
At their meeting upon Harry's arrival, Fudge said,"Tom will be keeping an eye on you for me." In fact, we don't see much of Tom after this, but Tom may have passed the word to the other shopkeepers of Diagon Alley, such as Florean Fortescue, to make the supervision of Harry's holiday unobtrusive.
Your own copy of Harry Potter and the Prisoner of Azkaban most likely says that Harry "was now facing three completely Dursley-free weeks." However, early editions of the book read "two" instead of three, but that doesn't tally with the dates of Marge's visit (the first week of August) and of the beginning of term (the first of September), so the text was officially corrected to read "three", and three weeks is now canon.