You'll want to fill up in Rawlins, as the fuel is much more expensive in Muddy Gap, and that's the only place to get fuel between Rawlins and Lander. Once you're outside of Rawlins and until you're in Lander, the only food on your route will be  gas station fare at Muddy Gap.

In Lander, there are plenty of places to eat, some of them quite nice. There's a micro-brewery there as well.

287 is a well-maintained, two-lane road with passing lanes on hills. From Muddy Gap to Lander, things get a little boring in spots, but it's otherwise a good road. In winter, the stretch from about 10 miles north of Rawlins to just south of Casper can be very tough sledding in blizzards and snowstorms.

If you're pulling a RV or are in a Class A, you'll want  to check on the winds before you leave Rawlins. The winds once you're outside of Rawlins on 287 can be quite fierce when storms are coming through. In the summer, you should be OK unless it is the later afternoon and there are t-storms coming through.

From Lander to Yellowstone on 26 is pretty interesting, and you'll tend to have some uphill stretches heading through Dubois. There's the National Military Vehicle Museum in Dubois, which is a lot more than it sounds like.

To get to Yellowstone, you have to finish pushing up to Moran - once you start getting up on top of the hill west of Dubois, you might want to take that part during the day, because you can run into (literally) elk in the night. Once in Moran, you'll take 191 north to Yellowstone, paying money to enter the NPS lands.