Orestes are you a lifelong resident of Oswego? I went to college in Oswego. Although they redid the area around the Oswego river there are a few grassy areas near the shipping canal and along the river. With Oswego's rich history from the War of 1812 and Fort Ontario there might be some good relics to be had. I had wanted to get back there for the harborfest but my friend, who lived there, recently passed away. Not having my friend there kind of made a trip to Oswego a bummer. Otherwise, I would think of making a trip up there and look you up.
I enclosed a couple of pics of the river area. If you're familiar with the river you might recognize the spots. If you walk the path along the west side of the river it will take you up to the power plant. Go past the power plant and you can get down to the river's edge. there is a little bit of woods that's accessible. Could be a good spot to detect. The locks and canal are on the east side of the river. The grassy areas along the locks might hold some promise. However, people might have already md'ed those areas already.
In any event , good luck to you. If I ever get up your way I'll try and contact you to set up a hunt.