Do you know where Riverside Dam is on the Duck River? It's very close to downtown Columbia. They just stocked a bunch of trout there yesterday - you should be able to catch a ton there right now and the access isn't too difficult. Be sure you have a trout permit in addition to your regular fishing license.
Here's a map for you:
http://www.tn.gov/twra/gis/troutpdf/...versideDam.pdf
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