Hello and welcome to the RTA forums !

One thing you will commonly see reading other threads is that we don't do 'best areas' or 'must see's' as these are the things that make each road trip a unique experience that's based on your own interests, of which you have told us nothing about. Chicago to LV is a 3.5 day drive so you aren't really going to have a lot of time for sight seeing. This is where a bit of research comes into play, to see what appeals to you and how you can organise the trip around it. You could break each day up into equal segments and have a little time each day to see things or you could get a 'hurry on' at the start and slow down for the second half of the trip. (Or vice versa)

Along I-40 you can enjoy some route 66 history with relatively small detours. There is Petrified forest and the towns of Holbrook, (Wig Wam Motel) Winslow, (Standin' on the corner) and the quirkey town of Seligman if you take '66 just after Ash Fork. You could opt to quickly see the south rim of the Grand canyon but that would take most of your 'free time' you actually have. This is where an extra day would be very handy for the journey.

Whatever you decide you should limit each day to around 550 miles per day to avoid fatigue setting in which will equate to 9-10 hours on the road including short rest breaks, lunch and to fill with gas etc. Once you have an idea of what you would like to see we can answer any further questions and help you put it together to make it as enjoyable as possible.