I agree, 20s-early 30s. Great deal for $20, you can't even get new plywood junk for that much! Even if you decide to spend some money and get it all nice again, it will still be less expensive than it would be to buy something that big brand new. And, you'll have some cool history behind it to boot. Not to mention, it's pretty awesome to be thrifty and re-purpose something and keep it out of a landfill!
Worth about $75 in my area in it's current condition. Get 'er all refinished and pretty again and worth about $250 or so, I would think. I agree, search for 20s vanity or 1920s vanity for comparable stuff.