Here are some of our favorites in Cody (I always keep notes on good places in my iPhone):
Cowboy Village Cabins: These are VERY nice log cabins built in 2006. Stayed there on a couple occasions. You can park your rig right in front of your cabin if you have a truck full of gear. My wife loved this place.
Proud Cut Restaurant: I second what Grizz said. Fantastic ribeye steak. Homestyle fries are great. Jumbo tempura shrimp are awesome.
Our Place Restaurant: Very good for breakfast.
Silver Dollar Bar and Grill: Awesome hamburgers.
Elk Horn Grill (Meeteetsee): My notes say "supposed to have a ribeye to die for"