Monique mentions a number of neighborhoods that are worth considering. I wrote a blog about these and other areas in the L.A. basin where good deals can be gotten for $250k to $500k which may help you. The link is below.
Also nobody mentinoed Mar Vista and Palms. Somes homes in these areas can still be bought for as little as $400k to $600k, including some areas west of ther 405 (San Diego) Freeway. You'll also find plenty of currunt listings in thse communities on my website. Please feel free to contact me to talk about the real estate options available in these neighborhoods. Best of Luck
I used to live in Silverlake and Echo Park. To me that was up and coming 10 years ago. For the Westside that would depend how far west you need to be. True Westsiders consider Mid-City and areas like Picfair Village and Faircrest Heights not the Westside. I think they are close enough to the westside to be a great option for anyone considering those areas. Culver City is great but pricey. The most affordable part of Culver City I would say is the area around the 90. Up and coming to me has a little more of an edge and is affordable too. My vote goes to 1. Picfair Village (where I live). New restaurants and shops are popping up left and right. It's a great area.
Faircrest Heights. Next to Picfair. Mid-City: Washington between La Cienega and La Brea.
If you have any questions about any of these areas, please let me know.
The Carrabba Group
I specialize in property on the Westside and would be happy to talk about the various areas/neighborhoods with you. My contact information is below.
Keller Williams Realty Westside