From my trip last fall, Old Faithful was definitely the least interesting thing we saw, but to each his own. I'd recommend the following:
Grand Prismatic Spring

Lower Falls (several viewing areas, I recommend Artists Point, Lookout Point, and Red Rock Point):

Hayden Valley

Lamar Valley

Tower Fall

Moose Falls

It all depends of course on your particular interests, are they wildlife, landscapes, waterfalls, hot springs, or geysers? If you're interested in wildlife, the two best places by far are Lamar Valley (in the northeast corner of the park, best place to stay nearby is Cooke City) and Hayden Valley. Lamar is the top place for finding wolves, and both places have grizzlies. Hayden Valley is also great for seeing bison. I also recommend going to visit the falls (both Upper and Lower) in midmorning for ideal lighting. I spent one night at the Old Faithful Inn, woke up at before sunrise, drove to Hayden Valley, saw my first grizzly there and a bunch of other things, then was up to the waterfalls by about 9:30 and stuck around that area for an hour or so and it was perfect. Then hit up Tower Fall on the way to Lamar Valley for a terrific afternoon of wildlife-watching. If you head down to the southern part of the park (as if you're heading into the Tetons which would be fantastic if you have time), don't forget to check out the less well known but beautiful Moose Falls not far before exiting the park.
Bottom line, you can't go wrong. Have fun!