There are a few ways to find old dumps...research your town's history at your library,walk creeks,ask any older town citizens if they remember where any were.See if any sanborn fire insurance maps are available from your town from the 1800's to early 1900's.The sanborn maps wont show dumps but will give you locations of old homesites and where they stood back then. Hope this helps.
Look at the Google earth satellite images of your area. Ravines, wooded patches, creeks, or riverbanks close to or within the town are always good places to check. With Google earth you can locate the older zones of the town, then look for topographical features within 1 mile of the old parts of the town where it is likely a dump site would have been located. Streams and ravines, since they have less of a steady erosive hydraulic force and are more shallow than rivers are ideal places to check first, since their courses probably haven't changed as much and the shards you see are more easily traced back to the source upstream. Old abandoned bridges (bridge pilings on the banks of a creek or river) are excellent places to look around, and have served me and others quite well. Explore cemeteries, because they were very often used as dump sites as well as corpse repositories. In fact, old cemeteries are often the best places to check, especially if there are creeks or ravines in the area.
If you tell us what town you are interested in exploring, we could offer some better suggestions regarding where to dig.
THANKS FOR ALL THE HELP. I LIVE IN THE BIG TOWN OF ROME GA. IVE BEEN COLLECTING BOTTLES NOW FOR ABOUT TWO YEARS AND I LOVE IT. EVERY PLACE I GO IM ALLWAYS THINKING MAN I BET I COULD FIND SOME BOTTLES THERE. THANKS ALL
City/County Parks are often put atop old dumps. Municipal golf courses as well. The closer to Downtown the older they likely are. A city I live near actually has "abandoned landfills" listed on their environmental web page however, no dates are included. Old City Directories might supply some information. Then there are always the family dumps in ravines, stream beds, etc. behind old houses or where old houses once stood...