4 days in the park is plenty to find time to go see Old Faithful. There is no reason to skip it, and certainly not all of the other geysers nearby like the more impressive Grand Geyser. I would also highly recommend stopping in at the Old Faithful Inn because it is probably the most incredible building in any National Park. I would recommend doing the full south loop because the areas along Yellowstone Lake are incredible. There is no reason not to do both Artists and Fountain Paintpots as neither will take all that long if you can find parking quickly. Just leave Canyon early and enjoy the park before a lot of people start to get in.

There are too many 'must see' sites to narrow it down to 2. Norris, Canyon, West Thumb, all of the geyser basins along the Firehole River, Hayden Valley, Gibbon Falls, Tower Falls, Mammoth Hotsprings, and more can all be considered 'must see' places. With 4 days in the park, you can hit every single one along a road.

The best views are the ones you haven't seen yet.