The best lodging in GTNP is Jenny Lake Lodge. It is too rich for my budget, so we stay at Signal Mountain Lodge. We like it quite a bit.
My favorite places in Yellowstone are Old Faithful Lodge and Lake Yellowstone hotel. Better start trying to book now.

In The Tetons check Jackson Lake lodge, either family cabins or the nonview hotel rooms. The least expensive rooms always go quickly. The snow lodge at Old Faithful is great, nice food court and great locations. Newer property. Book as soon as you know your dates. Go to the web sites for each park, I think its GTLC for the Tetons and Xanterra for Yellowstone, both parks managed by third parties. These are great parks, enjoy

We just did YNP/Tetons this past Sept - early-mid Sept - for 10 days. We spent 2 nights at OF Snow Lodge - great location, very nice rooms, decent food.
Next 2 nights at Mammoth Hot Springs in a hot tub cabin - loved the funky cabins and quiet location with bugling elk everywhere! And the dining there was very good.

Next 2 nights at Canyon in a pioneer cabin - great value for $60/night - pretty rustic but we had bugling elk and howling wolves all night long. Canyon area was the most crowded, had the worst food and was our least favorite area of the park, if we had to pick. But, it's a great location in this big park with easy access to everything. We could've easily spent more than 6 nights in YNP. Saw grizz & black bear, wolves, elk, coyotes, bighorn sheep, eagles, osprey, pronghorn, bison - it was incredible! But the thermal features are even more amazing!
We spent a night in Jackson on the way to YNP from SLC our first night. Then we headed back to the Tetons after YNP and spent a night at Signal Mountain - loved it. And great food on site. We saw lots of moose at Oxbow Bend, which is really close to Signal Mtn Lodge.

We spent our last night in SLC because the weather forecast was snowy and we didn't want to get stuck. While in YNP, we had gorgeous days - sunny and warm in the 70's, even low 80's! Nights in the 40's-50's. But cold and snow were coming just as we were departing so I'd suggest bringing warm clothes. We had not trouble making reservations and then changing them a few times so start planning now, reserve some nights in the park, then tweak them if you need to. You will fall in love with Yellowstone. We have lots of pictures if you're interested - C:\Documents and Settings\Sharon DiLorenzo\My Documents\My Pictures\Yelowstone 06

We visited Yellowstone and the Grand
Tetons in mid September this year.
We drove from Salt Lake City Airport and returned to the the airport.
We drove 1300 miles round trip.
I would recommend staying at the Old Faithful Inn,not the lodge.
We stayed in room 119 with the bathroom/showers across the hall.
No problem as the bathroom was never crowded. The meals at the Inn were very good.
We delayed obtaining reservations for dinner one night and had to eat at the lodge.The meal there was terrible.
We spent two nights at the Inn.
Be sure and take the ranger guided tours available throughout the park and at Jenny lake in the Grand Tetons.
The room at the Inn had steam heat.
Traffic was very light in September.
We next stayed at a Lake Yellowstone cabin.
The cabin was was large and warm but there isn't much to see.
I would instead stay at Canyon close by the Lower Falls of the Yellowstone.
Next we drove to Cody for two days .
We then drove back through the park to reach The Grand Tetons.
We stayed at a Colter Bay Village cabin and froze.
The only heat was a 12" by 18" wall heater that was worthless.
There was snow on the ground and it was cold.
Don't stay at the cabins.

My recommendations:
Two nights at the Yellowstone Inn.
Drive the north loop to Canyon for 2 nights. Drive out the north east entrance and take the Beartooth Pass to Cody.
Spend a day at the Buffalo Bill museum.
Then drive back through the park via the east entrance and spend several days at Jenny Lake.
I booked everything through the internet.
Xanterra for Yellowstone and Grand Teton Lodge Company for the Tetons.
Car rental from Dollar and Delta for airline.

Correction:
Two nights at the Old Faithful Inn! not the Yellowstone Inn.
I agree with sharondi as to places to stay . I was there shortly after her and missed the wolves and grizzles as we were at Lake Yellowstone which was too far south. It started to snow so we couldn't go north.

We were just in Yellowstone and GTNP this past September.

Our favorite lodgings:

Yellowstone - Dunraven Lodge, Canyon (for location/animal viewing, elk bugling, wolves howling at night)

Cody - Chamberlin Inn (excellent museum in Cody)

GTNP- Signal Mtn Lodge, we had a cabin for 2 with a gas fireplace. It snowed most of the time we were there. We LOVED watching the snow fall from our own private cabin in the mountains while the fireplace burned brightly!

If you don't stay at Old Faithful Inn, make sure you visit. We stayed there and also enjoyed an excellent dinner there.

You'll really enjoy all the elk around Mammoth Hot Springs.

Try going out of the east gate to Cody (beautiful drive), overnight in Cody and see the museum. Then take Chief Joseph to Beartooth, drive the Beartooth, then go back into the park via the northeast gate. All spectacular drives.

There are cabins, a Lodge and an Inn at Old Faithful. THE INN is what you want and what most people think of. If you cannot get lodging at the Inn, stay at the Lodge or cabins and eat at the Inn. The ambiance is wonderful!!!