Yeah, contact your local newspaper. I'm sure they'll have some routes open. I remember finding my route in an ad in the paper that told where the route was, approximate time it took to complete route, number of deliveries, and how much you made per week.
Some things to consider: The time your newspaper is published, and how many days per week you have to deliver. When I started our local newspaper was an afternoon printing meaning I could deliver after school. Also, at the time there was no Sunday newspaper. A few years later the newspaper switched to a morning publication, and seven days a week. Which means you'd have to deliver newspapers before school.
Also, when I started I had to go door-to-door to collect the money each week from each customer. I didn't really mind this, but it took twice as long. Now the newspaper makes people send the newspaper a check, and in turn, you get a check from the newspaper. This is a lot easier than collecting, but sometimes you get ripped off in weekly tips since the people don't see you.
Scope out the neighborhood of the route you're interested in. Is it nice or rundown? Nicer neighborhoods will yield better tips, but you'll have more crotchety old folks complaining about you walking on their lawn, etc. Good luck, if you have any other questions I'll try to help.