We have stayed at two of the parks in the Paducah area - Duck Creek and Fern Lake. Of the two, we MUCH prefer Fern Lake. They are about equal distant from the downtown area and the quilting museum.
We have visited the museum several times and are always impressed by the exhibits - which change frequently. One time there was an exhibit with 40 or more quilts all of which were over 100 years old!
Just off the square from the museum is a very nice seafood restaurant - Whalers Catch. Also, take some time to look at the murals along the flood wall and then go through one of the wall openings and look at the river scene - confluence of the Ohio and Tennessee rivers.
The one time we were in Paducah, we were staying at Fort Massac in Metropolis, IL, right across the river from Paducah. Fort Massac is an enjoyable state park and very pleasant to stay at. Being in Metropolis, we were able to easily visit the Superman Museum. Crossing the Ohio River on the bridge to Paducah gave easy access to all of the very enjoyable sites that Ray mentioned.