Arrive in town mid-afternoon. Find a church, put on a big smile, and ask for a floor and a ceiling. Or try the fire department.
In especially small towns, go to the only mini-mart in town and ask if there's a church/school/fire station where you can sleep on the floor, or pitch a tent out back. They'll know everyone in town, and someone can help out.
When all else fails, ask a policeman where's a safe place to set up a tent. Don't say "Camp," say "Set up a tent." Cops in small towns are usually bored, and will be glad to escort you to a city park, and even check on you later and make sure you're doing OK. They also might know a friendly church.
Bonus: You'll often get fed!