We only really try to do 500 miles (50MPH x 10 hours) on a given travel day. This gives time for road work, the unforseen breakdowns, etc. Have had several planned 500 mile days and ended up 14 hours due to the unforseen.
Depending on where you stay in Yellowstone, it can take a day to cover 200 miles due to the MPH in the area. Yellowstone is generally 35MPH (and about 1MPH with the animal sightseer jams).
Buffalo-Cody-Yellowstone can take about 4-5 hours alone. You only will average about 35MPH going up and down the mountains on US16 (slightly more if you go to the northern enterances and stay on I-90). US 16 is a very nice route and pretty easy to drive with good stops at Ten Sleep & Cody. There are long streches of flat land, but the moutain climbs/decends take the time.
If you stay in southern Yellowstone near the Tetons, coming up from Rock Springs WY you can miss quite a bit of the mountains and gain a bit more speed.