welcome to california!!
i don't want to be the bearer of bad news but $1,800/mo for a furnished 1 bedroom apartment is not realistic in santa monica. as previously mentioned, http://www.westsiderentals.com is the best site for your needs. they have the most listings and its an inexpensive membership, plus it allows you to search other nearby areas.
good luck with your search and your new beginnings here and if you have any questions once you arrive i'd be happy to answer them. all the best.
The SoCal Investment Real Estate Group
Sothebyâ€™s International Realty
License # - 01343854
Yesterday, today was tomorrow, and tomorrow, today will be yesterday. - George Harrison