i drove it last summer, went out across the north and came back through the..err..middle. On my way home I was mostly trying to make time since I had to be back at work by a certain date so I didnt do much other than the HWY. Anheuser Busch in STL was a stop that was close to my heart.
Not sure if you will be in the area but in Kanab Utah there is an outstanding burger joint called "Big Al's Burgers at the Junction".
If you are going to the GC you can go to the north rim or the south rim. The south rim is the more popular stop (i did not go there). The north rim is much less crowded and cooler (significantly higher altitude than the south) and has a lot of aspens and such....but it might not fit into your itinerary.
Not sure how far south you are driving but if you are coming through Kansas on 70 I did columbia, MO to Limon, CO (Actually I did it the other way around but w/e) in one day. Then took a day driving from Limon -> Boulder -> Estes Park -> through RMNP on Trail Ridge Rd (rt 34) and then back down to hook up with 70 again at Empire. This was a solid day for me because i spent a considerable amount of time in Estes Park shopping for souveniers and finding food and also stopping for tons of pics along TRR. This is a highly reccomended route if you have never been out west before.
Then you can get off of 70 near Cisco, UT and cruise down 128 to moab. Cool little town plus you can quickly go to Arches national park which is pretty enjoyable on a brief drive-through (stopping a few times to walk to a view point or something) as opposed to Canyonlands which is not nearly as accessible. If you go there I suggest you lookup Milt's for their ginormous open faces chili cheeseburger concoction. Then you can get on 191 which will take you back up to 70.
Another option would be getting off of 70 on rt 24 and heading down to hanksville and then continuing to Torrey where you pickup 12 (the burr trail) which is a really great drive down through capitol reef NP, grand staircase escalante, bryce canyon etc. At the end of 12 you can get to I-15 which will take you to vegas and beyond, or if you had more time (which you wont...) you could spin through Zion National Park (awesome).
All that being said, I think you would be best off if you went the northern route and just booked it on the highways from here to Wyoming and then took your time going off-highway from sheridan WY through medicine wheel passage and beartooth hwy (will blow your mind). Into YNP, down through GTNP, and then get back to the highways (via Idaho Falls or something?) after Jackson Hole.
edit: Also since I think ur going a southerly route...if you are in Colorado and its on the wya (not sure how it would be though) the million dollar highway is a nice stretch of road from Silverton to Ouray or some similar stretch along 550. Personally I was a little disappointed since it is supposed to be one of the most scenic drives in america and it was not as spectacular as some others I had enjoyed on the trip...but again, first time away from the easy coast, its pretty sweet.