In Deathly Hallows, at the beginning of Chapter 10, 'Kreacher's Tale', Harry enters Sirius' room and, after rummaging, finds the first page of his mother's letter to Sirius and the remnants of a photograph taken at or shortly after Harry's first birthday in 1981.
We know from canon that Sirius left Grimmauld Place around the age of 16.
'You ran away from home?' 'When I was about sixteen,' said Sirius. 'I'd had enough.' (OotP ch.6 p. 103)
From what he implies shortly thereafter, I've always assumed that he got his own flat after he came of age and inherited money from his uncle Alphard and hadn't returned to Grimmauld Place since. He only knew what happened to Regulus through what he heard from the other prisoners in Azkaban, not from what he heard from his parents.
'I never thought I'd be stuck in the house again.' (OotP ch. 6 p. 106)
When that letter was written to Sirius he was around 21-22 years old. He was living on his own around 5 years. At 22 he was arrested and incarcerated in Azkaban under a life sentence. How did that letter survive, let alone make it to Grimmauld Place? I know I'm probably not going to get a canon answer but it's always sort of bugged me a bit.
After two years on the run did Sirius arrive to Grimmauld Place to find in his childhood room a box of personal affects that aurors had confiscated from his flat and sent to his mother? Did Walburga see her son's conviction and feel deep regret for having disowned him after he had so brazenly murdered a presumed blood traitor and twelve muggles and decide not to incinerate his things but instead keep them locked away? I don't think so because I think a pretty significant portion of Voldy's sympathizers were more or less aware that Sirius hadn't sold out the Potters so possibly even his mother knew, but I can't be sure.
I'd appreciate answers that aren't too far-flung from canon, if anyone has any.