There are many answers to your situation. In the end, you will be the one that needs to decide what is best for you. First, there is nothing wrong with buying a property just in your name. You can always add your boyfriend later if it turns out to be a long term relationship. If you put him on title at the start and things do not turn out as well as you would like, it will be difficult to hang on to your hard earned money.
Second, is it a good time to buy? Most people think so. Prices have come down in most areas anywhere from 10 to 30%. Interest rates are as low as they have ever been.
Third, what is a good location? That depends on your taste. For some people that have children, the schools are the most important thing. For others, shopping or restaurants or entertainment are more important. For others, it is status of where they live. For others it depends on where they work. Only you know where you would be happy living. In general I would recommend Burbank, Sherman Oaks, Glendale, La Canada, Montrose or La Crescenta.
Finally, you need to understand that when you buy a property, you will need to plan on being there for probably a minimum of 5 years. It probably will take that long before the market recovers and it makes financial sense to upgrade. Some people like condo's or townhouses since they do not have to take care of the yard or they have amenities such as a pool or spa. Other people like their own home so that they can enjoy having a garden or they can make changes to their property without having to ask a Home Owners Association. Again, only you can make this decision.
I would recommend talking to a financial planner too. There are some tax advantages to owning a home. A financial planner or tax adviser can help you understand these things.
If you need help watching the market, please give me a call or send me an email. I can supply you information on properties in the Los Angeles County area. I also have a blog on Trulia where you can see other helpful information.
Tommy Lee DRE#01723594