Grizzly RV Park is two blocks from the west gate to YNP and has FHUs including cable and WIFI. That time of year is a great time to go, as crowds will be down due to the start of schools. Dress in layers, as it can be a bit nippy in the morning. And that's the time to enter the park. People arriving in the area typically arrive later in the day. The animals are more active in the fall since they don't have to hide in the trees in the heat of the day.
Is it more expensive? Yep. But the sites are roomy. And groceries and souvenirs are cheaper in town than inside the park. Cheaper, but not cheap.
And yes, I know its 12 miles to the Grand Loop, but it isn't a tunnel. One day, it took until noon to get to the loop. Buffalo jams and vehicles stopping to take pictures.
While in West Yellowstone, stop at the Grizzly and Wolf discovery center. There's an entry fee, but its your best chance to see either animal up close. And they're rescue animals. A Grizzly in the wild that kills cattle on private land is hunted down and killed. The center saves them and offers them to zoos around the country.