I think based on what you have described for your local area, The Westside is probably the area you would like, it has great transportation such as buses and light rail links and is conveniently located to about 20 minutes to downtown LA. Also the weather is much better as you are closer to the beach.
Here are some available properties for you:
Have a great day and feel free to contact me anytime.
Heather Paul, Realtor
Los Feliz is a lovely area in the eastern Hollywood Hills at the base of Griffith Park. Generally, it is an upscale neighborhood while the "village", as described previously, is cool and eclectic. See police crime maps here http://www.lapdcrimemaps.org/ - Have a safe trip if you are planning a visit.
Risa Liebster, RealtorÂ®
Keller Williams Realty