As for L.A., I don't know if it will re-open by the time you make a visit (their words: "late 2006"), but you'll definitely want to consider Griffith Observatory. In addition to the usual exhibits & other new/renovated offerings, a new restaurant decked out with glass panel walls will provide great views of the city and night sky. The gondolas over at Naples in Long Beach afford another romantic getaway ($60-65 now I think, was worth it when I took a date there).
Considering your limited time here, Olvera Street may also be worth a look. The atmosphere of the place and the neighboring plaza is generally cozy and romantic. There are some good (albeit overpriced) restaurants with patio seating looking out onto the quaint little street. Yeah, it's a bit of a tourist trap, but it's a nice quick way of experiencing a bit of more authentic Mexico in L.A. The plaza and Union Station across the street operate a bit more cohesively now thanks to some recent work. The grounds at Union Station are also very underrated, warm, and a nice place to frolic in if you find yourself in the area, IMO.
Like many ridiculously huge and complex places, there's just a sh!tload of cool things to do and places to see out here, you just need to know where to go. Hopefully someone else will chime in with other possibilities for you closer to the L.A.-area.
Oops, forgot all about Descanso Gardens! Well worth the $2 or $3/pop admission--a tranquil place to get lost in nature. This is actually my fav. date destination as women dig the roses, the rest of the greenery, streams, ponds, benches and shaded paths.
Congrats and good luck!