I live along Route 66, use parts for routine travels, have toured the route from Chicago to Flagstaff. When touring, I use "EZ66 Guide for Travelers" by Jerry McClanahan, published by the National Historic Route 66 Federation. When touring 66, I might take as much as three days to go 200 miles. Or you can run the whole route in three days, if you stay on the Interstate highways that replaced it.
There are still almost 200 miles of old 66 to follow in Oklahoma. Most roughly parallel the turnpikes, and later the Interstate highways, that replaced it. Although most of it is there, not many people follow 66 through Oklahoma, because it often doubles the travel time, more than triples the time if you follow the urban surface streets in Tulsa and Oklahoma City metro areas. Think miles and miles suburbs with traffic signals at 1/4 and 1/2 mile intervals, and we are into protected left turns, so if you catch a red expect to sit three to five minutes before you see green again.
What to see? That depends on your interests. I trained first as a historian, then later as a geologist, so I look for historical museums, and stop to study the rocks and the big holes in the rocks. But along Route 66, there are a lot of other attractions like 50's hotels, nostalgia diners and restaurants, a Cadillac Ranch, a big plastic whale, etc. I go to one of the restaurants (Talley's in Tulsa) simply because I like the food, but I've passed the whale at Catoosa at least 50 times and still feel no need to stop for a visit.
But many other Route 66 travelers are looking for the kitsch: the whale, the Cadillac Ranch, the 60 ounce beefsteak et al. Whatever rings your bell, which is why it helps to have a good guide.
Going to Kentucky, you will not get very far on Route 66. Last place to turn right and go to Kentucky is in Oklahoma, where you will follow US-60 across southern Missouri, through Cairo and into northwestern Kentucky. I've done that too, several times. It is a trip in itself, in many ways more interesting than Route 66. One of my US-60 trips took me all the way to Richmond, Virginia.