During Harry's fifth year, Sirius stays, most of the school year, all alone (except for Kreacher, but it's not exactly his favorite companion) at Grimmauld Place.
It seems sometimes Lupin comes and visits, since he's there when Harry use the Floo Powder to "go" and talk to Sirius :
Harry opened his eyes to find that he was looking up out of the kitchen fireplace at the long, wooden tabble, where a man sat poring over a piece of parchment.
The man jumped and looked around. It was not Sirius, but Lupin.
but that's all I can remember.
I find it's quite surprising, since Grimmauld Place was still the Order's headquarter, and, during the summer, it was quite a busy place : For instance, Hermione says in her letter:
There's a fair amount going on...
There are meetings, people coming (ang going) : Tonks and Lupin, Snape, McGonagall, Mundungus, once Dumbledore... (plus the Weasleys, who seem to live there for the summer)
Of course the kids went back to school, but what about all the Order's members that were constantly coming? And the Order's meetings?
Sirius would still miss going outside and really "do something", but at least he wouldn't have stayed alone with Kreacher, almost turning mad...