Topanga Canyon, I don't know much about it but I imagine it's a bit like, well, living in a forest in the mountains. Better hope your house doesn't burn down in a forest fire next fall!

Looks kind of remote, but at least there's some really nice scenery while driving to the more populated areas.
West Hollywood, I like it a lot which explains why I live here. The city was founded in 1984; before that it was just an unincorporated part of LA county that never joined the city proper. Somewhat useful website at
http://www.weho.org (Apparently we have an orchestra) It has a land area of 1.9 square miles and a population of under 40,000, so it's kind of a small community within the vastness of LA. Low crime, few homeless, and despite all the activity on the two main streets, residential streets are still very quiet and dark during sleeping hours. There is a pretty large gay population, something like 50%, which can be good or bad depending on your point of view; I just look at South Beach, San Francisco, and West Hollywood for concrete proof that it's a good thing, but just be prepared for some guys to hit on you if you're on certain parts of Santa Monica Blvd. after dark.

Though women certainly aren't hitting on me, so at least
someone is. Ha ha! Not as much of a problem on Sunset...
Of course the location is great; walking or biking distance to Sunset Strip and the stuff on Santa Monica Blvd., and Hollywood, Santa Monica, the Valley, etc. are all within reasonable driving distance. If you had a job in West Hollywood you wouldn't even need to leave the city limits, or own a car. You'll find cheaper apartments in, say, the Valley or the more questionable areas of LA, but rents aren't too bad and about the same as the other nice areas, and in any case you get a lot for your money and it's a great value, especially if you need a central location.
As for a motorcycle, it would be a great idea except for two issues. First is theft. Stealing a motorcycle is somewhat easier than stealing a car, and I don't know how much more it actually happens to motorcycles, but you might want to look into it, and get a tracking device installed in case it is stolen. You'll be better off if you have some kind of secured parking; I wouldn't recommend parking a motorcycle on any street overnight, every night. Second is idiot car drivers. Just last night someone nearly crashed into me by pulling in my lane when I happened to be going by. Minor accident with a car but could mean serious injury or death on a motorcycle. Not that there are a lot more idiot car drivers in LA than in the rest of the world but if you otherwise wouldn't be driving a motorcycle you should think about the risk.