Most geysers are a short walk, or a short hike. There are longer hikes to different geysers, and if you are like me, you'll probably find yourself wanting to take them all or as many as possible. I was lucky enough to spend a week there last time I visited so plenty of time to get out and take many of the hikes.
A safety warning, always stay on the park paths. Especially while you are in the areas of the park that have the active geysers. This is not one of those times you want to wander off the beaten path, they are marked to keep you safe.
So, regardless of the view you want, or the selfie you want to take. Don't be an idiot, because if you wander off the path and get too close and find yourself burned or worse you'll only have yourself to blame.
Old Faithful isn't the only predictable geyser in the park, you will find many others that you can hike to and plan your schedules around to see.
I actually find this National Park beautiful, it has so many different things to see and do. You can enter in through Montana or the Wyoming side, and I highly recommend taking the scenic drives and a few days to do them.
Have you visited Yellowstone before?