Do NOT miss Jackson Hole ...
If you are looking to allocate time, do NOT plan on going through the Teton's quickly. For an active outdoors enthusiast, the Tetons is THE place to be. Yellowstone is for tourist toads. If you like mile-long back-ups for every elk sighting (they are everywhere) and looking at boiling mud, Yellowstone might be interesting (I'm kidding, sort of). Really though, the mountain scenery is spectacular in the Teton's everywhere you go. In Yellowstone, Yellowstone Falls is worth seeing and so is Old Faithfull (just you and about a million other people sitting in a grandstand area on the edge of a mud flat). Basically, Yellowstone is a giant collapsed caldera and the mountain scenery is just not that great. The attraction is all the geophysical oddities, which don't hold my attention for very long, so I tend to get bored there. Once I've seen one boiling mud pot, the next 15 attractions, which are basically all about the same thing just doesn't get me as enthused.
The hikes are nothing to write about, except that I did get pretty spooked when I was hiking with my kids about 8 or 10 miles off the road up near the source of the Little Firehole River - thinking we would run into a grizzly at every turn. I don't remember seeing people on bicycles (Harley's - millions of them - but not road bikes).
Hikes in the Tetons are epic. Take all day to hike Cascade Canyon (take the Jenny Lake Ferry to save your legs) or Death's Canyon. You'll never forget what you see. A short hike down to Phelps Lake off the beginning of the Death's Canyon trail is a nice refreshing place to cool off in the water.
http://www.trails.com/activity.aspx?area=10116
http://www.jacksonholewy.net/trails
Road biking in Teton National Park is the kind of place where people come specifically for that activity and you see groups whizzing by on road bikes everywhere. My wife and I were mountain biking and we literally had to go thru a herd of buffalo because my wife was hungry and she wasn't going to be stopped. I told her it wasn't a great idea to get anywhere near one of those big fellows, but he was only about 15' off the trail and wasn't moving. So she paid no attention to me and I had to follow ... luckily he didn't make a move but Sue said he had a strange look in his eyes when she rode past.
We took an introductory (all-day) kayak lesson on the Snake River. After learning techniques on a flat back-eddy for a few hours, we were guided from town (Jackson to Hoback Junction) downstream several miles with Class 2 the whole way. I flipped over a few times trying to do tricks and show the great-looking instructer that I was into it

... Sue had no problem staying upright the whole time. But we did get to ride a lot of fun rapids the whole way. Below Hoback Junction is where the rapids get more intense if you are into that sport.
Basically, Jackson is about the coolest town you will ever visit and there is so much more to do in the Tetons than anywhere else, that is where I would plan on spending most of my time (if not all of it) ... but that's just me ...
My daughter says Hegben Lake in SW Montana is really nice ... about 15 miles by 4 miles so it nicely sized. She lives in Big Sky and goes there frequently. The fishing is supposed to be really good there.