Carla,
I used to be an "antiques dealer". I also live in Los Angeles.
Going to tag sales is a big thing especially in the area of LA that I used to live in. Lots of old homes with families that are clearing out their families belongings.
Every person has a junk store that they drove past for the last 5 years. You just need to recognize them.
I also shop (for my own home) at the Design Within Reach stores in the big cities. They have authorized copies of pieces for sale. The are very expensive. You may be able to find another store that copies this style for a lot cheaper.

These pieces are getting to be very expensive if they are the true designs of these designers. One may find knock offs in garage sales.
Time and energy, and sometimes money can help.

That is true about the "junk" stores, Boop. Some of my favorite antiques have come from junk shops, and some things that are not antiques at all, in quite good condition, that were just what I needed at the time. One of my favorite "going antiquing" stories is the time I found a gold Depression glass double candlestick in perfect condition mixed in with about a hundred old jelly jars in the attic of an old junk shop. I then found its match in an antique store in Oklahoma about a year later. What I saved on the one at the junk store helped pay for the one from the antique store! They are quite beautiful and are gracing my mantle at this very moment.

Hi Carla!
I find a lot at antique stores, sometimes thrift stores, and there is always Ebay.
Happy shopping!

I agree with the above posters. Best bet is to hit thrift stores and garage sales if you don't want to pay ridiculous prices for new copies of mid-century modern. I find it's the out of the way places that have the best stuff. I found a fabulous blonde living room set complete with kidney shaped coffee table at a Salvation Army outside of Pittsburgh. I still kick myself for not buying it but at the time I couldn't afford the $350 they were asking for it. If I saw it today I'd buy it in a heartbeat. I think as time goes on it will be harder and harder to find these items because it seems demand for them is increasing and they get snatched up quickly.

Check out ApartmentTherapy.com, they have posted links to manufacturers and places you can buy similar pieces.