Today, the hot commodity in vintage appliances are stoves, especially stoves in good working order. Any vintage appliance, including an old washing machine, is best valued if it's in great condition. Missing parts, dents, rust, scratches, and other mars will detract from value. Learn about your old washers including age, maker, name of the specific product, and the year it was made.
Vintage washing machines with squared tops and ringers appear on eBay for between $100.00 to $500.00 asking price. Check sites like eBay but check the sold prices as asking price may be unrealistic. Check out the Old Appliance Club online for more information, parts, etc.
There are people who restore vintage appliances for sale. See if you can find one in your area as they may be interested in buying yours. Selling on Craigslist is an option too. Selling through online auction sites may be difficult due to shipping costs. But some folks don't care about shipping costs.
Whatever you decide to do, once you learn about your product, make sure that you take excellent photographs. Show details of problems as well as close-ups of interesting features.