I think the better question is "What kind of a house do you want"? If your credit is in as good a place as your income appears to be then your options are far less limited and you are in what some would call an enviable position.
I am guessing that you are wanting an idea of your purchasing power and that question is truly best answered by a lender. I can help you find the property that fits your needs and your ability to purchase but I rely on my client's lender to help determine what the value we are working with should be.
In West LA there are cute bungalows built in the 20's and 30's, great condos and some more sprawling properties, it really just depends on which part of the city you want to be in. If you want to be in WeHo proper, (closer to Santa Monica Boulevard, past La Cienega and heading toward the beach) there are more multi-family homes in that area than single family ones. That doesn't mean that there are not some great houses nestled in there, but the vibe of the area tends to be more social.
If you haven't already spoken with a lender, then I would suggest that this is probably one of the first places you should start. Speak with a couple different folks to see who you "click" with and who has the best product to service your needs.
You should also be looking at meeting with a couple different Realtors to see who you would like to work with. Your opportunity to purchase, especially because of the financial position you are in, has truly never been better in recent years.
If you have any additional questions, or if I can be of any further assistance, please do not hesitate to get in touch.
Take care and have a great day!
Tisza Major-Posner, Realtor, IVPG Realty (213) 392-4084 or (909) 837-8922