We've been planning our summer trip, which is going to take us to two places outside of Yellowstone - Red Cliff Campground on the Gallatin River north of the park about 45 miles, and Yellowstone Valley Inn, along the North Fork of the Shoshone River between the East Entrance and Cody. We'll be able to visit the park, and I plan on taking the drive on the Beartooth Highway.
While I've been doing my research, I came across this: a live webcam of Old Faithful! It refreshes every 30 seconds.
Old Faithful Webcam
What fun! If you're patient, you can see Old Faithful erupt!