Sirius didn't know what to make of this place. On the one hand, he was glad to be out of prison, but on the other hand, he felt like he deserved to be there. No, he didn't directly kill James and Lily, but he may as well have. He was the one who suggested they use Peter as the Secret Keeper instead of him.
To make matters worse, there was a woman here who looked exactly like, and claimed to be, Lily. She couldn't be. He knew that as well as anyone. The second he heard about Lily and James, he had gone to their house. He'd seen their lifeless bodies. He'd handed Harry, his godson, off to Hagrid before going off to hunt Peter down. There was no way this woman could be Lily and it angered him to think that she was impersonating his dear, departed friend.
He stayed inside for the most part and did his best to avoid the network, but he needed to get out, he needed to breathe. He decided to go for a walk through the park. Thankfully, it seemed to be empty. He ran his hand through his long hair and let out a sigh, sitting on one of the benches.