There is only one known room, the living room. And only a few things are there, due to Sonic's lack of money.
The living room is where Sonic spends most of his none-working hours. He spends his time watching his Poster, because he has no TV.
Sonic later bought a frame for Poster, but sadly Poster was destroyed by Mario and his goons.
When Sonic became the boss of the Mob, he moved out and stayed at the Mob office until Tails destroyed it. Sonic then put a garrod willkins poster and is back to square one. When Sonic returned his house seems to be more dirty, such as the top of the checkpoint bulb is broken, due to the battle with Mario at the climax of Season 2