We went just this past October.
We stayed at Big Bone Lick State Park (great little park with Wooly Mammoth and Mastadon bones!) and a herd of buffalo.
I would agree with Cameo Phil on spending 4 to 6 hours or perhaps a full day. We took our time and visited almost everything, including the zoo. It also depends on when you go. We went in mid-October during a weekday. Kids were in school and big tourist season was over. If you go on a weekend and during tourist season, you will experience much larger crowds and therefore more wait time/standing and waiting to view exhibits. It is truly and incredible experience, and what I liked is that the exhibit never says "this is exactly how they did it", but rather it says "these are some plausible ways that they COULD have done it." Things like harvesting water from the rain on the roof to fill urns, pumping fresh air throughout, etc.
You may also want to visit the (relatively nearby) Creation Museum in Petersburg, KY as well.
Some photos to give a perspective on the size of the Ark: