Pete, at the risk of sounding like I am teasing you, I would reccomend that you start at your local historical sociaty. Find out what the heck has gone on in the past around your fair city of Beaumont. You learn the history.......you find the goodies. I am serious.
If you need a quick fix, hit the local city park. Parks always have a bit of clad, a ring or two, and maybe even some older coins and relics. Again, find out how old the park is and start from there.
I think they found oil in Beaumont once. The man just would not give up until he struck oil. There has got to be tons of places to hunt. How many hunting clubs date to way back when, or boat launch sites. The school bleachers wound be a prime spot. There are so many abandoned homes on the back roads. I wish sometimes I could hunt the Old Thomas place outside Evadale. There were tons of party's held there to all hours of the morning. Got to be lots of pocket change just waiting to be dug up. And the one thing Texas is not lacking in is Bar parking lots. Well unless of course its in a dry county. Happy Hunting.
Mike