If your house-buying budget is about $1,000,000 here are three properties in your price range:
Atwater Village: Duplex, each unit with 2 bedrooms, and backyard. Asking $999,000.
Echo Park: 2-bedroom front house with 1-bedroom back house. Asking $998,000.
Lincoln Heights: Fourplex with parking and plans for 2 additional units. Asking $1,069,000