^ On that time frame, you won't be able to do much. First of all, in that area, you have to add 15-20 minutes on top of each hour google 'thinks' it will take you. Driving around up there is extremely time consuming.
Diamond X can easily take you all day, so depending on if you just play 1 18 hole loop, or if you have guides, or if you take your time, can really determine what time you leave Billings. Billings to Yellowstone is (if I remember right) 4 or 5 hours away minimum.
Once you are in the park (check out a map), the roads roughly follow a figure 8 pattern. The points of interest are all roughly 45 minutes to an hour apart. If you have never been to the park, you might as well check out Old Faithful and a few of the thermal features around there. If you take Beartooth Highway in from Billings, you will pass through Lamar Valley as soon as you enter the park, and that is a premier location to see wild animals. After that, complete the loop counter clockwise to Old Faithful and check all that out. Spend the night in Old Faithful, Grant Village or Lake Village, and the next day you can complete the loop by driving along the lake, and check out the dg course there if you want. It's easy to get to Cody, WY from there (89 miles 2 hours), which will have you on the fast track back to SD. If you have time that day, you can head north of lake a little bit to Hayden Valley, which is the other big wildlife viewing area, then head back to lake to get to Cody. That's about the best whirlwind trip of Yellowstone I can think of.
Just if your wondering:
Mammoth Hot Springs is cool, but kind of out of the way and ultimately skippable. It DOES have one of the few places you can soak in thermal water though, if that's what your looking for.
Canyon: That's where Yellowstone Falls is. Totally a Griswold Family photo opp, but not much else.
Norris / Madison: Basically drive right through, they are more road intersections than anything else. One has a geyser basin but there are so many more in the park that you can basically skip these.
Grant Village: A few lakeside thermal features, but really no geysers.
Lake Area: A marina and a hotel, some cool thermal features nearby.
Old Faithful: Where they geyser is, as well as many other geysers and hot pots. There is a section of river here that you can go into that is thermally heated and kinda cool.
I miss Yellowstone
