Where the royal is held is not a great area, but there are no hotels there anyway. The hotels in the western side of the downtown loop (around Bartle Hall) or the Sheraton and Westin at crown center will be your best bet. Not sure which have shuttles, but the royal I think usually has shuttles to downtown and union station - which will get you to hotels in these areas.
And yes, there is a race that weekend at Kansas Speedway (in the chase), so I imagine hotels will be at a premium.