1) Westside: tends to run more affluent, access to the coast a huge plus; excellent eateries, design/decor retailers, and a wide range of architectural styles to choose from whether renting or owning. We used to live in Venice and the neighborhood is still amongst our favourites in all of LA, with a mix of high and low integrated into the neighborhood. It can get crowded in the summer months, but we used to live with one of the foot traffic only sections near Abbot Kinney and the mix locals and visitors became an asset, not an annoyance. Santa Monica seems to be popular amongst non-locals who move there for the coastal lifestyle and general safety, and is particularly great because of the eateries nearby (Musha, Bay Cities), museums like The Getty, and design/furnishing stores galore. Marina del Rey is popular amongst single working professionals with many rental opportunities. Malibu if you can afford it and enjoy outdoor activities such as hiking, surfing, etc. Culver City probably the furthest east of the Westside locations that seems bustling and growing; quite a few friends are moving here for the urban-suburban mix, vibrant art gallery scene, and the anchoring Helm's Bakery district where restaurants seem to open every week.
2) The Valley: mostly suburban and where we personally grew up. What we like most about the Valley, at least alongside the outer edges near the surrounding mountains is the hiking. You can really get away from the crowds and enjoy parts of LA where hidden waterfalls, creeks and canyons can give you a daily mini-vacation just outside your door. Not many people know, but O'Melveny Park in Granada Hills is the second largest park in LA right after Griffith Park. The Valley tends to be more of a family style lifestyle, but there are great eateries out there, especially around Encino and Studio City. Cultural activities are a bit more limited, but it's improved considerably and a drive over the hills into LA is just a short drive.
3) To avoid a HUGE debate amongst locals, we're just going to mention Silver Lake, Echo Park, Los Feliz and Hollywood as nothing but those neighborhoods (there's an ongoing argument of whether they're "eastside" or not; we personally call anything east of the 101 freeway "eastside"). These areas range from posh to more urban. We were born in this area, just south of Echo Park, and have called Silver Lake home for over 8 years now since moving back from SF. We'd argue for a New Yorker, Silver Lake, Echo Park, Downtown Los Angeles may offer the best lifestyle transition due to its urban setting, access to museums and eateries, and the general cultural hodge podge that makes LA life such a joy. It also doesn't get super hot or blistering cold over here. And a big plus is the architectural choices in our area, ranging from Victorian homes of Angeleno Heights to super modernist homes sprawled across the Hollywood Hills down to humble modest sized studio apartments like our own in Silver Lake. If you have any specific questions about Silver Lake or Los Feliz, we can give specific details about any questions you might have (rent, eateries, population makeup, etc).
4) East of Downtown and beyond: these areas are becoming more popular with all the hidden hillside gems and historical neighborhoods that stretch out to genteel Pasadena into ethnic neighborhoods like Monterey Park. We actually love heading out eastward, but don't know enough to give you personal accounts of living out there (Grace can vouch for Pasadena).
Readers, feel free to share your own hoods! We're forgetting great locales like Burbank, Glendale, Atwater, Century City, Westwood, Agoura Hills, etc. Fill our friend in about what makes living in your area wonderful.