One of the nice things about Yellowstone National Park is that most of the famous attractions are easily accessible from the loop road that runs through the park. Of course, you can take more time to hike around and get a feel for the area, but Artist Point, Yellowstone River and Lake, Old Faithful, and Mammoth Hot Springs can easily be done in a day.
I would recommend making sure you get to experience Bear Tooth Pass Hwy, which I thought was just as impressive as Yellowstone itself! Coming from Cody, it's a little out of your way, but if you take the Chief Joseph Hwy, it hooks up with Beartooth along the most scenic part of the drive. (This is assuming you're doing a summer visit, as the highway is closed in winter.)
I'd dedicate the first day to the drive and maybe Mammoth Hot Springs, spend the night at Roosevelt Lodge* or Mammoth Hot Springs Hotel and Cabins and then spend the second day exploring the park, hopefully waking up in time to catch the rainbows at Artist Point.
*Roosevelt Lodge is in the northeast corner of the park - not sure why it's showing up where it is.
Well, Polly hit all the big ones, so I will have to add some of my favorites, of course Norris Geyser Basin is always my favorite, I will see Steamboat Geyser erupt one day. Just above Beryl Spring which is between Madison Junction Rd and the Norris Geyser Basin is an extinct geyser bed, which is kind of cool and only 1/2 mile off the road (up a trail). Some of the more interesting geysers are behind Old Faithful, such as Castle Geyser and Whirligig Geyser, both are just a little off trail. I could list enough to fill a week, but with limited time, those are some of my favorites.
I reccommend going through the Old Faithful