Art, welcome to iRV2.
We are visiting Yellowstone now and are staying in Grizzly RV Park in West Yellowstone. The campground is only about half a mile from the West Entrance. Grizzly is a little expensive (with FMCA discount, we're paying about $44 a night for a back-in site with full hookups incl. cable), but the price isn't that bad for a tourist area and the campground is VERY nice.
We came from Cody several days ago, and I would not recommend trying to visit Yellowstone from there. Driving times within the park are very deceiving because of traffic. Speed limits in the park are 45 mph (or less) and most people drive slower than that. Also, things come to a complete stop if there is any kind of animal anywhere within view of the road. Therefore, adding the extra driving time from Cody to the East Entrance of Yellowstone would make for long days. From Cody, you drive over the Absaroka Mountains, which isn't bad without the RV; but even without the RV, travel is a lot slower than on the interstate.
As Maverik says, if you want to stay in the park, make sure you have reservations. Fishing Bridge RV Campground is the only campground in the park with electric hookups, and they are probably booked well in advance. It may be easier to get a site in one of the other campgrounds, but many of the sites in those are limited in the length of RVs they can accommodate.
Yellowstone and the Tetons just to the south are well worth the trip. Enjoy.
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