The most direct route, meaning most interstate would be: Denver-Cheyenne-Rock Springs-Jackson-Yellowstone/Grant, as a parent this is a pretty long haul in one day. I drive Jackson to Cheyenne pretty regularly, on this route and its under 6 hours, with a quick stop in Rock Springs for bathrooms & food. When you add in Jackson-Grant and Denver-Cheyenne and you've added another 3-4 hours, for a total of 8-10 hours depending on stops. I agree overnighting just makes sense. On this route, I would overnight in Jackson, and enjoy GTNP on your way up to Grant via the south gate the next day. . Jackson is a good choice as there are lots of options for lodging and restaurants, but it is the most expensive place to stay. An alternative route with less interstate would be Denver-Cheyenne-Rawlins-Lander/Riverton-Dubois-Yellowstone, Lander/Riverton (5-6 hours from Denver) would be a good overnight, although another 75 minutes would put you in Dubois, which is about 2 hours from Grant Village (103 miles). This would allow you to get up in the morning and spend the day enjoying scenery as you drive through GTNP and the south gate of Yellowstone. This route has some fabulous views of the Absarokas, the Pinnacles over Togwotee Pass. The Tetons will be spectacular, but you'll get those with either route. So in summary either Jackson or Dubois would be my choices for an overnight stop on the way to YNP from Denver both about 7 hours from Denver. If that's too much car time, stop in Lander or Riverton.