Exercise For Free?

Where are some good areas or trails to walk or hike within reasonable distance from downtown Jackson?

I am not really looking for concrete walks with manicured lawns or indoor tracks.  I am looking for wooded areas with dirt trails that wind and climb - maybe with a chance of some nature encounters.

Lefleur's Bluff has a nice walking trail, but it also has an entrance fee - so walking that daily is too expensive ($3.00 a day builds up quick).

The Natchez Trace  provides some nice trails, but since I live in Brandon, leaving downtown, the Trace is the opposite direction from where I need to drive.

Brandon City Park is a nice place to walk, but it has a short trail and it gets boring after a few dozen times around.  Vance park is worth some investigation, but it is still paved and in a residential neighborhood.

So, if you know of any nice woodland walking / hiking trails between downtown Jackson and Brandon, let me know!

And, hey, if you know any good walking trails in the area - whether they meet my needs or not - post here and let othrs know too!