As with everything in real estate, it depends on how much you want to spend. In the immediate downtown area, 2-3BR homes are available, but prob not what you're looking for in terms of "walk-able neighborhoods." If you can go a bit further west there's Echo Park & Silver Lake with the trendy shops and restaurants and mid to upper priced homes....about 20" to downtown. A little further west is beautiful Hancock Park with charming Larchmont Village area shops and restaurants...but the homes tend to be quite pricey. If you can go a bit north of downtown I've had great luck finding affordable family homes, particularly in Eagle Rock, Mt. Washington, Highland Park (straight up the 110, half way to Pasadena, about 20" from downtown) that are nearby shops/restaurants. And then, even further north is Pasadena where there are some very "walk-able" areas. Usually you will pay a premium to be close to a walk-able area.
Let me know if you are looking for a Buyer's Agent to assist you in your search. Best of luck!
Keller Williams, Los Feliz