•  Clark Center Recreation Park (formerly Carbide Park)  - This is a jeep road at the back of the park that is steep in places, but not too strenuous.  About 5-6 miles roundtrip with Melton Hill Lake views.  One can swim at the park after a sweaty ride.  There are also a lot of picnic tables.
• Third Creek Trail -  I think it now starts on Sutherland Avenue near the Post Office and goes past Knoxville landing to Ned McWerter Park under the overpass.   Maybe 14-15 miles roundtrip.  You can stop at Calhoun's for a beer or lunch.
• Maryville Greenway - This is a wonderful trail that is very well maintained by the cities of Alcoa and Maryville.  There are many access points, and if you do the complete roundtrip, it's a little less than 18 miles.  The trail is asphalt and has many runners, bikers, walkers and rollerbladers on it.  Nearly the whole trail runs beside a creek that flows through Maryville.

If you think you can ride a bike well, just check out this Google Video.