So the wife and I did a trip from Denver to Custer SD, to Livingston MT to Whitefish and finally Sandpoint ID. We had been to Yellowstone/GTNP/Jackson a couple of times. Based on what you are seeing/doing if you haven't already you should get a national parks pass it will be cheaper than paying at each park. So places that I think you should check out:
1) Badland NP
2) Custer State Park - very gorgeous scenery
3) If you must - and by that I mean if you have never done it before and do not think you will do it again in your lifetime - stop at Rushmore - go at night and see the lighting of the monument then get out and never think of it again - sorry I just thought Rushmore was worthless!
4) DO NOT GO TO CRAZY HORSE - in showing pictures that we took of Crazy Horse a month ago to our neighbors, they pulled out photos that were 5 years old and there was no difference - I am not sure they are actually working on completing the Crazy Horse Monument - the tribes are just collecting the money.
5) There are two caves near Custer - Jewell Cave and Wind Cave - we only had time to do a Jewell Cave tour (we picked Jewell based on the recommendation of a friend that said if you could only do one Jewell should be it - this cave is mammoth - the Entrance to Jewell cave is something like 15 miles west of Custer SD - there are individuals that are exploring the cave system that think the cave will reach under Custer.
6) We did not get to eat here - but several people told us to eat at the Black Hills Burger and Bun Company in Custer - the wait was 1 1/2 hours - we declined even though the guy walking out said stay in line it's worth it!
7) After Jewell Cave we drove west and then northwest to see Devil's Tower - there is a mileish long hike (paved) that encircles the Tower and the Tower is different from each side. I wish we would have had more opportunity to explore around Devil's Tower - the area around the Tower was really pretty and not what I expected.
8) Again, as someone mentioned above, on the way northwest from Devil's Tower towards 90 you can stop at the Little Big Horn National Monument. I was happy that we got to stop there, you don't need much time there (maybe an hour) but I thought it was a nice stop. Also chatted with a PSU grad from NY at LBHNM - we are - everywhere!
9) I have never done the drive through Red Lodge but I have heard very nice things.
10) As someone stated above - to maximize your time if Yellowstone you need to plan where you will be staying so that you are not driving around the figure 8 all day.
11) We really liked Livingston, MT - small town - ranching area just 55 miles north of Gardiner, MT (the north entrance to Yellowstone). If you stop in Livingston, go have a drink at the Murray hotel - recommended by Bozeman panic fans in the lot at Red Rocks as well as Anthony Bourdain (at least he did recommend it). Old hotel with ghosts and all.
12) We also enjoyed Bozeman, very different from Livingston even though they are only 25 miles apart. Small college town - we should all be fans of small college towns right?
13) Since you are also going to GTNP - I will tell you that I liked the hiking and solitude of getting into the Park on the west side - you would drive towards Grand Targhee ski area and there is a road that takes you towards the west side of the park. Then you hike in. While you are on the west side of the Tetons check out Driggs and Victor and the Teton Valley. Less crowded and more laid back than the Jackson side of Teton Pass.
14) Finally, Glacier - words cannot describe the majesty of GNP!!!!!! I am making an assumption here so if I am wrong I am sorry, but I assume that you as with 99.99999999% of visitors will only see the Going to the Sun Road portion of the park (still worth it!!) my only advise is get into the park early - like 6AM by noon there will be no parking available in the park at major stops along going to the sun road.
If you are going to do any backcountry hiking in YNP/GTNP/GNP - be bear aware and prepared! Have fun!