The main city that you see in Route 66 Texas is Amarillo. Obviously slightly famous for the Tony Christie song - we certainly made use of the sign posts for them to "show us the way".
The first place that you want to head to is The Big Texas Steak Ranch & Brewery. This is the home of the 72oz steak challenge. If you manage to eat the whole steak in the space of an hour then you get the steak free! The "Big Texan" is also a great place to spend the evening. There are lots of other things to see on the site, plus also lots of arcade type games to take part in. The Big Texas also has a hotel and this would be one of the hotels to stay at on the route. This would allow you to stager your way after you've done the steak challenge!
Moving into Amarillo there are a number old buildings to see. One of those is the old Paramount Theatre. This building is no longer a theatre but an office block - however its Art Deco frontage is something to look at.
In the 6th Street Historic District area of the city there are lots of diverse shops, restaurants, and galleries along the original Route 66 Texas that's well worth a stop.