Sounds like you've got a great trip planned.

Echoing what someone said earlier, I think it's a great idea to pick an area for the day and spend all (or at least most) of the day there. There are a lot of 'tour bus tourists' that you'll see get out of their cars, walk the 200 yards to take their picture, then get back in the car and go to the next location. Sure they'll see some of the highlights of Yellowstone, but they really miss out on a lot.

You could spend a whole day in the Canyon area taking the walk/hike along the rim on one side and down to the brink of the lower falls, then go around and take the walk along the rim on the other side. There are pullouts along it and a lot of folks will do the drive 1/4 mile, get out, take pictures, get back in car, drive another 1/4 mile, get out again..... routine, but the trail there runs that whole length and then some and I'd definitely recommend doing that instead.

Same thing with the Norris area, if you take all the boardwalks / trails around the Norris geyser basin and check out the museum at the Norris campground that'll fill an entire day. Same at Mammoth and the Old Faithful area and (well you get the idea). Take it in rather than rushing to the next picture spot.

When you're staying at Old Faithful in addition to the boardwalks in the immediate geyser basin I enjoy the short hikes to Black Sand basin and Biscuit basin (if you look at a map of the Old Faithful area you should see where they are) rather than getting in the car and driving there. It's just a nice way to get away from the crowds, away from the loud motorcycles and streams of RVs and cars without being too far away from anything.

If you get a nice warm day consider spending the afternoon swimming in the Firehole River (swimming area is along the Firehole River Drive). Warm(er) water and just a really neat experience.

I think all of the whitewater rafting companies also offer calmer float trips. I know we took one of those when I was a kid and I'm sure it's still ongoing. I would probably prefer to wait until it gets close (maybe 3-5 days out) to book that so you can see how the weather looks. An 80 degree sunny day on the river is heaven, a 55 degree rainy one is quite the opposite. While in Jackson be sure to stop by the town square to see the elk antler arches made from antlers dropped during the winter on the national elk refuge nearby.

Have a great time, I'll be there in late June and I can't wait!