Dustbuster... I hope you don't mind someone from New York who lives in Montana helping out a little.
I don't know how big this town is you live in, but you're going to have to get out and talk with some folks... network, have conversations, and research!
Research is more than HALF the battle (and half the fun) to landing on top of a great hunting spot. I read local history, talk with old timers, I talk with locals who have been around forever or friends with antique parents living in antique houses. I spend time in my library reading old papers and periodicals, yearbooks, and local festivities announcements. I've looked at more maps than I thought could possibly exist for my area, combed the back roads, and burned a lot of fuel exploring the outskirts of town. I compare old maps to new maps and overlay them if possible. Swimming holes, homesteads, hillsides, big huge old trees, picnic grounds and racetracks, fairgrounds, church sites, dance halls, tepee ring sites, battle sites, ball fields, fraternity halls, retreats, forts, trails, scout camps, other camp sites, and everyplace else that folks gathered to do things 100 + years ago.
You have to walk up to property owners and talk to them and ask permission... it's a scary thing for some folks, but there is a high success rate! In Montana there is an on-line program to find out who owns what parcel/property... otherwise your county clerk can tell you - as well as tell you all about every previous owner.
I spend as much or MORE time researching than I do detecting - but it pays off.
And, always remember, you're only going to find stuff where folks have been losing stuff. It's not always easy and sometimes there just isn't anything to find - so you can never get discouraged! There just might not be anything to find right around you!
Modern parks, churchyards, playgrounds, soccer fields, ball diamonds and tot lots get old fast if yearning for older coins and relics. You should be exhausting all efforts to chat with the folks who own the oldest houses in the county... and be willing to drive a while too, research - research - research!
You've also had some great advice above... we all look forward to your finds!