Part-way through Goblet of Fire Sirius returns to Hogsmeade, the village in which he'd successfully evaded Ministry of Magic capture in for the duration of the previous year. The reason that he wants to be in Hogsmeade at the time is to be near Harry:
He grinned up at Harry, but Harry returned the grin only reluctantly.
"What are you doing here, Sirius?" he said.
"Fulfilling my duty as a godfather," said Sirius.
Goblet of Fire, chapter 27, Padfoot Returns
We learn that Sirius is living in a remote mountainside cave, which takes around 30 minutes to walk to from Hogsmeade. My question is why Sirius felt the need to use the mountainside cave at all. Sirius has several requirements from a dwelling place:
- It must be secretive and impossible to stumble across so as to evade Ministry capture.
- It must be near Harry (to fulfil Sirius's intrinsic desire to be paternal to Harry), and therefore have good access to Hogwarts.
- It must be big enough to allow him to store a contraband Hippogriff.
- It must allow Sirius to gain basic supplies (such as food and access to news of the outside world).
It seems to me that the Shrieking Shack meets these requirements just as well as if not better than the mountainside cave does. There was plentiful room for Buckbeak in the Shack and indeed presumably the squawks and cries given out would've only have enhanced the folklore surrounding the Shack amongst nearby wizards. And the Shack is not only literally closer to Harry (surpassing the 30 minute trek into the village that Sirius otherwise faced) but has a direct tunnel link to Hogwarts that Harry, Ron and Hermione could've freely used to visit Sirius and pass him food. His life as a stray facing the cold of the mountainside and living off scraps seems completely unnecessary.
The whole cave plan as it turns out was Dumbledore's idea:
"You are not Sirius' only correspondant," said Dumbledore. "I have also been in contact with him since he left Hogwarts last year. It was I who suggested the mountainside cave as the safest place for him to stay."
Goblet of Fire, chapter 30, The Pensieve
One possible reason for avoiding the Shack is that it's not safe for Sirius once his hideout is disclosed in Prisoner of Azkaban. However, only Harry, Ron, Hermione, Dumbledore, Lupin, Wormtail and Snape know about secret passageway through the Whomping Willow post-Prisoner of Azkaban. All of these people are pro-Sirius, apart from Snape and Wormtail - and neither of those two have reason to know/suspect that Sirius has come back to Hogsmeade. The Shrieking Shack is therefore still a perfectly safe place to live during the events of Goblet of Fire.
So why did Sirius/Dumbledore overlook the Shrieking Shack when it had served Sirius so effectively the year before?