In Chandler, you'll find the Route 66 Interpretative Center, which you can't miss – it's on a big curve heading into the city. You can relax here, too: among the displays are seats from Model As, Jeeps, and '64 Mustangs, as well as a few beds you're allowed to lay down upon.
About eight miles past Chandler you head through Warwick, now essentially a ghost town where U.S. 177 crosses Route 66. Despite its low activity level, there's still something great to see in Warwick: the Seaba Station Motorcycle Museum. Over 65 bike models from 1908 to the present adorn several rooms in the museum, with a gift shop in the front offering a wide variety of collectibles, shirts, and refreshments — which are definitely needed when the hot Oklahoma sun beats down. Seaba Station has a "ride-in" the third Sunday of every month, weather permitting.
Beyond Chandler and Warwick, Route 66 crosses Interstate 44 and rides north of it for a ways into the next town, where you come across an interesting blend of old and new.