We have stayed at Bridge Bay (around '86), it was our first trip to Yellowstone. Moose would walk through the CG back then. Don't think many are left in the Park, none by Bridge Bay Area. The Fires killed their habitat a Ranger told us in our last visit in 2010. Should be able to all the loops from there, we did or could have.
A Little of What I have on
Yellowstone & Tetons. We have always stayed in the parks themselves. Never felt we had to have electric hookups. Never had a reservation before going, always found a place to stay.
More on Wyoming:
We've gone by Thermopolis, WY twice to do a soak in the hot spring water at the State Bath House. Very neat.

We overnighted in the Wind River Canyon in Aug '09 & at one of the Boysen State Park campgrounds by the lake some years ago.
Hot SpringsCody Walmart was our neatest Walmart Overnight Site yet:

Cody is a neat place. In Cody, try to see the Buffalo Bill Historical Center with Five Museums Under One Roof.
http://www.bbhc.org/The Cody Chamber of Commerce has a nice Visitor Center (full of information) & with a really nice art gallery.
http://codychamber.org/visitorcenter.htmlNever been to it, but they have a Cody Night Rodeo with rodeo performances every night June 1st through August 31st. Gates open at 7:00 p.m. with rodeo action starting at 8:00 p.m.
http://www.codynightrodeo.com/ And a Cody Stampede Rodeo July 1 to 4,
http://www.codystampederodeo.com/ Likely to be too out of your way, but just in case:
East of Billings on I-94, we drove by
Pompey's Pillar not knowing what it was in 2009, about 25 miles east of Billings, Montana, on our way to Yellowstone. "It bears the only remaining physical evidence of the Lewis and Clark Expedition, which appears on the trail today as it did 200 years ago. On the face of the 150-foot butte, Captain William Clark carved his name on July 25, 1806, during his return to the United States through the beautiful Yellowstone Valley." Might be worth a stop, if time allows.
On 1-90 between Billings & Sheridan, Little Bighorn
Battlefield Nat'l Mon't has a special place in history. Not far from Sheridan.
Also off I-90 in WY,
The Site of the Fetterman Fight and
Fort Phil Kearny.
We like to find places like these to see & to spend time on the road. Overnighting Sites & Sights in the
Douglas & Wheatland Area. Includes Guernsey & Fort Laramie Area.
Guernsey State Park -------
Fort Laramie National Historic Site ------
Oregon Trail Ruts and
Register Cliff North & East of Yellowstone area & somewhat out the way perhaps: On the western side of North Dakota 27 miles east of the Montana state line, Theodore Roosevelt National Park is very worthwhile to see. The South Unit entrance is in Medora, ND. Medora is accessible via Interstate 94 Exits 24 and 27 in North Dakota. T. Roosevelt is a really nice place to see Bison, at times even in the campground. We visited both units that year. North unit is more into the oil boom area. Road was good back then, but after getting more into the boom area, lot of truck traffic. Maybe worse now?
The colorful Little Missouri River Badlands provides the scenic backdrop to the park & home to a variety of prairie plants and animals including bison, prairie dogs, pronghorn, elk, mule deer and wild feral horses.
T. Roosevelt.
The Painted Canyon Visitor Center is located 7 miles east of Medora on I-94 at Exit 32.
The ND Badlands are in TRNP as mentioned. Very neat shapes & colors. Not been to the SD Badlands, can't compare them.