​Yellowstone covers 3,471 square miles and has 5 entrances.  This is not a park that you can visit in one day.  The best way to see the park is to stay in different areas so that you don’t spend more time driving in your car than you do exploring the park.  You would be doing yourself and the park an injustice if you just drive straight to Old Faithful, snap a photo, and head out without taking time to explore everything else Yellowstone has to offer.  All major areas of the park are connected by the Great Loop Road.  I recommend a 5 day 4 night stay in the park. What you see on each day depends on where you enter the park.  Since the main road is a loop, just plan to drive in either direction to complete the entire circle.  If you don't want to change hotels, the Yellowstone Lake area is probably the best location to use as a home base.  

Model Itinerary

Old Faithful Area: 2 Days
Start at the Old Faithful Visitor Center where you can get a park map and find out about any Ranger Activities for the next 2 days.  Park Ranger’s offer a variety of programs, such as, guided hikes, narrated walks, and talks about the history or wildlife of the area.  It is definitely worth the time to take one of the Ranger walks through the geyser area so that you can learn more about everything you are seeing. The main attraction in this area is the Old Faithful Geyser which erupts at predictable intervals each day.   Geyser Hill Loop (1.4 mile easy walk) is one of the easiest and most interesting trials in the area and passes several thermal attractions.  Take Observation Point Trail (2 mile easy/moderate hike) for a spectacular view of Old Faithful Inn and the geyser area.  You might pass some curious marmots on the trail.  The trail begins at the Old Faithful Boardwalk past Solitary Geyser.  Many books say not to miss the 7 mile hike on Fairy Falls Trail to see Grand Prismatic Spring!  It’s a short drive to the Lower Geyser area and the Fountain Paint Pot Trail (.5 mile easy walk) to see the mud pots.  Book two nights at the Old Faithful Inn and make dinner reservations for one night at the Inn dining room.  If the Old Faithful Inn is full, try nearby Old Faithful Snow Lodge.
Mammoth Hot Springs and Norris Geyser Area: 1 Day
Hike both loops of the Norris Geyser Area. The Back Basin Loop (1.5 mile easy hike) takes a boardwalk to Echnis Geyser which erupts several times daily.  The Porcelain Basin Trail (.5 mile easy hike) passes some unique geothermal features.   
The highlight of this area is to drive around the Upper Terrace Loop and then take time to walk the Lower Terrace Interpretive Trial (1.5 mile easy hike) to see the hot springs.  If you still have time in the evening, drive to Gardner, Montana to see the original park entrance. Book 1 night at the Mammoth Lodge or if that is full there are hotels available in nearby Gardner.
Lamar Valley and Canyon Area: 1 Day
Take a scenic drive on Northeast Entrance Road off of Great Loop Road through the Lamar Valley which is where you will find herds of buffalo, elk, and if you’re lucky some of Yellowstone’s wolves.  You do not need to drive the entire road, just drive until you have seen plenty of wildlife, then return to the Loop Road.  
The Canyon Area of the park is commonly referred to as the Grand Canyon of Yellowstone.  There are many hiking trails in this area, but most of the viewpoints can be reached by a short walk from the parking lot.  Make sure to stop at the overlooks of the North Rim, Lower Falls, Artist Point & Tower Falls.  Upper Falls View  (.3 mile easy walk) leads down from the parking lot to the Brink of the Upper Falls overlook near the river and waterfall.  Hike the entire trail or just part of the North and South Rim Trails (easy footpath along the canyon rim) for better views of the canyon.  For a different view, walk to Inspiration Point (moderately strenuous descent down 57 steps) to an overlook with views of canyon.  There are hotel rooms available in the Canyon Area, or spend the night at nearby Yellowstone Lake Lodge Western Cabins.
Yellowstone Lake: 1 Day
Yellowstone Hotel offers an amazing breakfast buffet to start your day.  Yellowstone Lake is so large that is creates its own weather.  You can walk around the lake trails or take a boat ride out on the lake and enjoy the water.  Don’t miss a stop at the West Thumb area for a short hike along the lake to see geysers.  There are hotel rooms available in the Canyon Area, or spend the night at the Yellowstone Lake Lodge Western Cabins. ​
Grand Teton National Park:
Grand Teton National Park is located just 31 miles south of Yellowstone so this is a great park to add to your week long itinerary.  We flew into Jackson Hole, Wyoming and spent a few night there before we headed out to Grand Teton and then Yellowstone.