I live in the west side. I've been in LA for 8 years and I'd love to find new romantic things to do here. I feel I'm going to the same place over and over again now (Malibu winery, Abbot Kinney in Venice, Manhattan Beach downtown). I'm all about restaurants, places to visit, etc...
When i lived in Santa Monica one of the things my girlfriend (now my wife) and i loved to do was rip up the PCH on Tuesday afternoons to hit Duke's Malibu. We'd sit at the bar at The Barefoot Bar, eat fish tacos, and chit chat with the locals who run the gamut from crusty Malibu lifer surfers, to car salesmen from the valley. Its not fancy, its unpretentious, and it always ended up being really fun to laugh and check out the surfers or paddle boarders.
Try a sunset Gondola ride! You can take them down in Naples or Newport Beach. http://www.gondolagetawayinc.com/ . They will even put a message in a bottle for you in case you'd like to surprise your sweetie (proposal anyone?)... It's a lovely experience. Also Terranea Resort down in Palos Verdes has some really nice dining options, very romantic dinners.. all except Nelsons. The outdoor deck off the main bar has firepits with incredible views of the Pacific. good luck!
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Yamashiro is a restaurant and bar above Hollywood with beautiful gardens and a spectacular view. It's a great place for a drink and it looks from recent reviews like the food has improved greatly from the old days.