Congratulations on your decision to purchase a home in Los Angeles!
I believe if you want to extend your Visa, you need to file a request with the U.S. Citizenship and Immigration Services.
Here is a link to more information about this: http://www.uscis.gov/portal/site/uscis/menuitem.eb1d4c2a3e5b9ac89243c6a7543f6d1a/?vgnextoid=cab23e4d77d73210VgnVCM100000082ca60aRCRD&vgnextchannel=cab23e4d77d73210VgnVCM100000082ca60aRCRD
I am a real estate agent with Rodeo Realty and I specialize in the Los Angeles area. Please feel free to contact me at (310) 717-1321 or JamieTian@RodeoRE.com with any questions or concerns.
I would be happy to provide you with a list of available properties that fit your criteria by email and set up appointments for you to view any properties you are interested in during your visit to Los Angeles.