Should I lie to my co-workers about what part of the country I am originally from?

I have lived in Los Angeles for a little over a decade but I grew up in New York City. I recently started a new job and while no one has asked me yet where I'm from, I'm concerned someone will ask. I have always felt embarrassed and ashamed to be from New York City and I have always been worried that people would think less of me if they found out I was from there. Knowing these facts, should I lie and say I'm from LA (even though I'm not) or should I tell the truth and say I'm from New York, even if it runs the risk of people thinking less of me?