Can't help on camping with hookups, never have done that in Yellowstone or Tetons. Many seem to use West Yellowstone for hookups. Fishing Bridge RV Campground is the only one in Yellowstone with them. Colter Bay RV Campground has them in the Tetons.
We have been four times to Yellowstone & three times to Tetons, never had a reservation, never had to sleep in leaves either. Ha!
What I have on
Yellowstone & Tetons. I would agree with spending more time in Yellowstone for the same reasons.
More Misc. Info ------
Horse RidesPerhaps, the horse back rides would be a win. We did one once with our kids. Horse rides of one and two hours in length which are available at Mammoth, Tower-Roosevelt, and Canyon.
On another trip we had our canoe with us, enjoyed canoeing on Luis Lake (from CG to the Shoshone River & up a way) & Yellowstone Lake (from Grant Village to Geyser area by West Thumb.
Boating, Canoeing, Kayaking We canoed in some of the lakes & in the Snake River in the Tetons as well. Canoed in the Ox Bows on the Snake (calm waters).
There are Float Trips, a Jenny Lake Shuttle, Scenic Cruises:
http://www.nps.gov/grte/planyourvisit/boat.htmWent on a few Ranger programs as well.
We did some fishing on one trip in Yellowstone as well.
However, the scenery is so grand & wildlife so plentiful if into photography one can really enjoy finding & capturing memories with a camera.
Lot of stuff around Canyon Area & somewhat central for branching out to see the sights. Just south is the Hayden Valley. Be sure to drive the Grand Loop Rd through the Hayden Valley (usually see Bison there) from Canyon Area to Fishing Bridge Area. The Lamar Valley has been a wolf watching mecca since the wolves were reintroduced in 1995. It has Bison as well & we have seen bear there as well. This is in the Tower Area east toward the NE Exit of the Park. All the loops have neat things to see.
Tetons are really neat as well. Several lakes. The Colter Bay Visitor Center and Indian ArtsMuseum by the Colter Bay Campground in the Grand Tetons is really a neat one.
In 2010, we came up through Salt Lake City. We used US 89/91 from Brigham City (just north of Salt Lake City) to Logan then up to Bear Lake (US 89). Then North & East to Jackson & on to Moran (Tetons). US 89/191/287 leads into Yellowstone. 302 mi, 5 hours 43 mins. to Moran.
Salt Lake City to Moran Via I-80 E to Evanston & WY Routes 16/30/89 to U.S. 89 N: 305 mi, 5 hours 20 mins.
Salt Lake City to West Yellowstone: 320 mi, 4 hours 44 mins. I-15 N and US-20 E I-15 N into Idaho, exit at Idaho Falls.
My son's in-laws rented a Class C in Billings a few years ago to join my son & family in Glacier.
From Billings to Gardiner (North Entrance to Yellowstone): 170 mi, 2 hours 37 mins. I-90 W to U.S. 89 S.
Billings to West Yellowstone: 231 mi, 3 hours 53 mins. using I-90 W and US-191 S.
At least I remember it being Billings. However, I believe they drove to Billings. Therefore, Billings info would be Moot.
Salt Lake City must be the closest place to rent.