Looking for a used car on a 10k budget

Hello, I don't know much about cars so detailed responses would be appreciated.

Things I'm looking for:

1. 10k budget, a bit over is fine.
2. Reliable, good safety rating, decent mpg.
3. Planning on moving to Los Angeles so something good for city driving like in LA.
4. Something small/medium sized w/ 4 doors (been mostly looking at sedans).
5. Automatic.
6. Used, to lower the cost.

I drive a 2007 ford focus hatchback w/ 150k miles that is on its last legs (power steering fluid leak that costs more to fix than what the car is worth). Been mostly lookin at the Honda Civic and Toyota Corolla. I don't really care about cars so aesthetics or it being fun to drive don't really matter. Just looking for something to get me from point A to point B in a good manner. Thanks!