I am wondering why you don't want to go the auction route. Large collections can be easier to move at auction. However many auctions will not accept collector plates! That is because the market is poor. Just think, in the 1980s and 1990s collector plates were heavily advertised on TV with promises of future rewards. Items marketed as limited editions were produced in the thousands if not tens of thousands. No one can predict the future and if someone promises that they can you better not believe it. So tons of collector plates were amassed by Baby Boomers who were into the collecting craze of the time. Now those same buyers are selling in order to downsize, or leaving their collections to their children. The market is glutted.
Older collector plates from the early 1900s can be quite valuable. Some special interest newer plates still sell well so it depends on what you have. Royal Copenhagen Christmas plates from the 1970s, for example, can be found at thrift shops for $3.00 a piece while older plates can sell for a nice price. You can't even give Norman Rockwell plates away.
You must learn the current values of each item before you try to sell them. Look for sold prices at online auction or sales sites.
You can try to sell your plates on consignment if a shop will accept them. Consignment shops will, of course, want about one third of the sale price to cover their expenses and gain a profit. Setting up a table at a flea market can be inexpensive and a lot of fun. You can also have a yard sale or an estate sale. Advertise your sale on Craigslist, or an online site like YardSales.net or YardSaleSearch.com. Mention the best of your wares on the sites.
Of course there are also online sites like ebay and etsy or specialty sites.
The value of each piece will determine how to sell the plates. If you learn that a particular piece is quite valuable you won't want to go the yard sale route.
How you choose to move your collector plates depends on all these variables in addition to your own comfort zone.