There are lots of places to ride.
Check out
www.kybikerides.org. There's about every ride imaginable posted.
The Louisville Bike Club hosts rides every day. The "recovery" and "slow and easy" rides are a good place to start.
Southeast Christian Church hosts rides every other week or so during biking season.
My favorite is out Tucker Station Road to Rehl Road and English Station. Fairly light traffic except at 8 and 4 weekdays.