Both Room & Board and DWR will have many pieces representint mid-20th-century design; and they both sell via their websites and are easy and convenient if you want a specific piece and they carry it. Shopping exclusively from them (and their contemporaries) won't give you the most unique or distinctive interior though. You could risk having too much of a catalog look.
If you live in a major metropolitan area, you will likely find lots of "vintage" (meaning mid-20th-century design) pieces via Craigslist or local "antique" stores. When I was refurnishing my apartment in 2007 and spending a lot of time on Craigslist, it seemed like the Chicago-area was rife with mid-20th century stuff: Herman Miller, Eames, Knoll, Steelcase, etc., etc., etc.
Check out our very own
Cool furniture, design objects and desiderata thread. Follow the links on stuff that catches your eye and go from there.
Also, in addition to Better Living Through design, a few other blogs I bookmarked in 2007 were
I don't read them much anymore, but I do remember them being at least good jumping-off points for finding other blogs, designers and vendors of modern and contemporary design and furniture. Oh, and Dwell magazine too. I know it gets a lot of flack, but I pick up a copy and just flip through the pictures and advertisers; just like browsing 20 vendor websites in one issue.
Some additional vendor websites to check out:
My personal experience when doing the big refurnishing project in 2007 was this: there are a lot of web resources related to modern and contemporary design out there. It's pretty easy to spend a relatively small, but focused effort in surveying the landscape and seeing a whole lot of pictures of stuff to help narrow the field into the type of stuff you like and you don't. Then, you can focus on vendors who carry the stuff you like.
For me, after about 2 month of reading, looking and seeing pieces in real-life, I was ready to start buying. YMMV.