As far as seeing the sights in both Grand Teton and Yellowstone, your best bet would be to camp at the Colter Bay Campground and day-trip into Yellowstone. We did that this last spring, early June, leaving our site at Colter Bay Campground around 7:00, going to Grant Village, Old Faithful, on to Norris Junction and then up to Mammoth, over Dunraven, down to Canyon, over to Lake and then back to Grant Village and to Grand Teton. Got home around 7:00 in the evening. Lots of travel and sights, all in one day. About 25 miles to South Entrance to Yellowstone and then a ways past Lewis Lake Canyon and Lewis Lake before getting to Grant. If you were to take two or three days to travel around Yellowstone, this would certainly be the way to go, compared to camping around Cody and driving in each day. This is just my opinion, but we have been doing this for over 50 years and find that it's a great way to go and being in Grand Teton is a wonderful way to spend time and well as sightseeing around that park as well. Also, coming from Colorado the trip over to Rawlins, up to Lander through Dubois and on to Grand Teton might be shorter than the trip to Casper, Shoshoni and up to Cody. Might check your maps to see which is shorter.