Here are some suggested activities for visiting Yellowstone with younger kids or teenagers who really aren't into hiking or fishing.  You can do all of these in two or three days if you take the time to plan out your trip.

Cruise the Hayden Valley looking for wildlife.  If you can get out in the morning at sunrise, you can see many animals without the crowds.  You might see a fairly large herd of bison crossing the Yellowstone River on a cold, clear morning.  The fog over the river, plus the vapor snorting out of the bison as they swim across is pretty amazing. The Hayden Valley is one of visitors' favorite places on earth.  Combining the sunrise over the Grand Canyon of the Yellowstone is a great way to start out your morning, plus you can get back in time for breakfast, and to head out to do something else.

Cruise the Lamarr Valley looking for wildlife.  You should drive up to at least Soda Butte before you turn around if you're travelling east up the valley.  Never be afraid to stop and ask what people are looking at, particularly those with spotting scopes.  They are usually friendly and helpful pointing out what they are looking at. Get out at sunrise if possible.  Continue  on to Cooke City for breakfast, which makes for a great way to start the day.

Grand Canyon of the Yellowstone...go to every pullout you can, particulary Artist and Inspiration Points.

Sit on the deck of the Old Faithful Inn, having an ice cream cone as Old Faithful erupts. 

Go swimming in the Firehole River swimming area.  Face it, travelling with teenagers, they get bored with animals and take them swimming. It breaks up the routine.  The kids love it, plus if it is 90+ degrees that day it is a great way to cool off after walking around the boardwalks at Old Faithful.

Grand Prismatic Spring at the Midway Geyser Basin...simply awesome every time you see it. Even your kids will love it.  You can even wade in the Firehole River here.

Walking the boardwalks around the Old Faithful area.  Avoid the walk to Morning Glory Pool as it's not worth it, particularly if you have whiny children.  The West Thumb Geyser Basin is small and easily hiked around, plus it's on the shore of Lake Yellowstone so it's also very scenic.  Kids can get overwhelmed with all the thermal features and can get bored with it after a while.  Short doses really help.

Hiking down Uncle Tom's Trail at the Grand Canyon of the Yellowstone.  Worth every step back up.

Hiking up Mount Wasburn.  The view is awesome.  Read the guidebook's suggestions on this hike...too many people don't take water or head up there in the afternoon when the winds can really pick up.

Hiking the Storm Point Nature Loop near Fishing Bridge...this gives you a great view of Yellowstone Lake when you don't have a boat, plus the opportunity to spot wildlfe is good.  This can be closed to bear activity so check with the rangers at Fishing Bridge.