Just checked: Google Maps says it's about .8 miles from the Grand Desert to the front of the MGM Grand complex. Across LV Boulevard from there is New York New York, which has some rides your kids might like. If they're 19 to 32, maybe not.
Diagonally across LV Boulevard from MGM Grand is the Ex Caliber, then the Luxor pyramid. Further south is Mandalay Bay, which has a lot to see and do. By the numbers, from Grand Desert to Mandalay Bay is approaching two miles.
I'm thinking some sort of transportation will save your feet and time. Uber and Lyft might be the easiest way to go, since you can call for what you need, when you want it.
Dave