Decent 16" bikes do turn up at Goodwill. I also got one from Craigslist. Unless your 4 year old is giant, chances are that some 16" bikes will be too big and some will work, so make sure he's with you.
We also just got 2 refurbished bikes from our local bike coop. We are a low-income family and our coop gives away age-appropriate bikes, fixed up by volunteers, to kids from self-defined low-income families who attend a bike rodeo. Awesome program!