Everyone has different ideas about what makes an attractive investment. However, I'd like to offer a couple of ideas that focus on the financial aspects of buying property in L.A., assuming that we're talking about long term investments.

The most important thing to remember about investing in L.A. is to never buy a mediocre property. There is a startling potential for appreciation on properties in the L.A. Basin proper and beach cities. This is going to get a lot of people mad... but everywhere else is strictly second rate. If you're not taking advantage of this when you buy a property in Los Angeles you should probably be investing somewhere else given the kind of deals that you can get in places like Las Vegas, Texas, and Florida right now.
This being said, L.A. isn't a great town for profitable multi-unit properties, especially from Downtown to the beach, which is some of the most expensive real estate in the country. Single family homes can't be rented profitably anywhere in the city and multi-unit properties that run close to, or in the black are unheard of in all of the upscale areas from the Beach Cities & Westside to the Hollywood Hills.
The best investments in the L.A. Basin are found in an arc from Downtown and Koreatown to mid-Wilshire, Picfair (Pico & Fairfax,) and the Baldwin Hills. This is essentially where the 'gentrification' of the L.A. Basin halted a couple of years ago. Profitable multi-units can occasionally (though not routinely,) be found in these neighborhoods and the potential for appreciation is considerable. I expect the Los Angeles basin to go high-rent from the beaches all the way to Downtown & USC, and southward to the LAX International Airport glide path over the long-term as the market starts to get healthier.
This leaves Long Beach. In my opinion, Long Beach (and San Pedro to a lesser extent) are the best investment opportunities available in Southern California. There are usually a more than a few profitable properties available as well as a hand full of really attractive investments on the market at any given time in these undervalued communites around the habor. As the only affordably priced coastal real estate from San Diego to Santa Barbara, the full revitalization of these cities is inevitable and in fact, already well underway.
Profitable muti-units by the beach with a lot of potential for appreciation, what's wrong with this picture? Maybe nothing.
Please feel free to contact me If you'd like more information about investment properties in Los Angeles. Best of Luck.
Andrew Jones REALTOR / Office: 310-399-3740
Venice, CA
CA Lic# 01131486 / NV Lic# S.0071586

'Andy Always Brings Out the Best in a Changing Market !'
http://www.jonesresortproperty.com/

Many years ago my sister purchase a home near USC for her daughter and her friend when she went to school there.