O.K. so it seems you're skipping Rocky Mtn. and on to Grand Teton/Yellowstone....
In our opinion and even with our bad knees, the Tetons have much better hiking than Yellowstone. There are trails of all abilities which will lead you to beautiful lakes and vistas. Only if you want to really mountain hike will you find the rugged ones. The Tetons also has very nice biking with a long paved bike trail and mostly flat or near so.
Since you mentioned dry camping is o.k. with you, we really like Gros Ventre campground in the Tetons. It, along with Colter Bay campground each have 300 non-reservable sites and if you plan it to drive in during the morning or early afternoon you'll get a site. We always have with our 40' motorhome. If you want hookups then Colter Bay RV is right next door to Colter Bay campground.
I'd recommend taking the gentle float trip down the Snake River in the park. You just might see a moose in the water with you. We did!
For Yellowstone, why not stay IN the park itself for the best overall experience? Fishing Bridge RV has full hookups. Otherwise, we've stayed in Bridge Bay, Madison and Mammoth campgrounds - dry camping. I wouldn't recommend try to bike ride in Yellowstone. There are no shoulders on the road, no official bike trails and lots of BIG animals on and along the roads.
Each national park has an excellent web site so study it thoroughly for things to do, road information, camping and hiking information. Have a great trip. We've been to all of them often and keep returning for a reason. :)
Grand Teton Nat'l ParkYellowstone Nat'l Park
