Invite someone over (someone who is your friend or of you Rep Group recommended). If they like your place a lot they will give you a "housewarming gift". If they do not, get their relationship to 90 to 100, leave the room (they will be gone), go back, and invite them again.

Berkeley Clodd: 3-Card Monte Table
Busta Cruz: Punk T-Shirt
Cannonball Coleman: Music Stand
Crystal: Magic lamp with comfy bed and toilet
Darius: Uncle Suede's Cane
Dr. Maximillian Moore: Periodic Table of Elements
Dusty Hogg: Burning Spoke Sign
Ewan: Street Light
Giuseppi Mezzoalto: Orange Pedestal
Lily Gates: Liberty Statue
Luthor L. Bigbucks: Bumper of his car that goes on your wall
Mambo Loa: Voodoo Dan Doll
Phoebe Twiddle: Lawn Flamingo
Polly Nomial: Khroniton Reactor
Sharona Faster: Megalodon Tooth
A free item will appear at your house every thirty game days:

30 days: Mardi Gras Mask
60 days: Jack-o-Lantern
90 days: Pilgrim Gnome
120 days: Candy Cane