E.T.
Yellowstone is gorgeous! Start making plans now if you want to stay in the park. Everything books up really early! Right near Yellowstone is Teton National Park that is spellbinding! (I grew up 100 miles from Yellowstone so I'm a little biased.)
Probably the best time to go is late June. Late August would also be another time to go. The weather is still pretty cool and it seems to not be as busy. July tends to be pretty busy. Avoid early August. When the Sturgis Motorcycle Rally is happening in Western South Dakota, Yellowstone is bombarded with bikers.
If you are driving out from California, come into Wyoming near Jackson, Wyoming. Spend a day or two in Jackson and then drive up through Teton Park. Some friends of ours rented a condo in Teton Park and said it was really great. It was a good proximity to Jackson Hole, Teton, and Yellowstone.
If you want to stay in Yellowstone, the cabins at Old Faithful are pretty rustic, but not bad. It is also a little more centrally located. I would suggest staying there if you can get a reservation or I would suggest staying in a couple of different places in and out of Yellowstone. Maybe a day or two in Jackson. Maybe a night at Mammoth Village. Maybe a night at Old Faithful. Maybe a night in East Yellowstone, Montana. It would be a long haul up to Glacier National Park, but going through East Yellowstone would be probably the best route. If you were up to it, going east out of Yellowstone, about 50 miles from the East Entrance is Cody, Wyoming. It was the home of Buffalo Bill. They have a fabulous museum of the West and a night rodeo. You'd get a taste of the Old West.
Be prepared to do a lot of driving in Yellowstone. The top things to see are pretty spread out. Be prepared to hike. There are easy trails and boardwalks to walk on, but some of them are a couple of miles round trip and some of them are extremely steep. Be prepared for rustic. Unless you are staying at Lake Lodge ($$$$), things are far from being 5 star hotels. And please, take the warnings about wild animals seriously. Please follow the signs that tell you to stay on the path. Lots of people do really stupid things and get injured or even killed. And straying off the path is not only dangerous, but it can cause permanent damage to some of the more fragile areas of the ecosystem. Yellowstone is a beautiful place to visit, but it is wild. And the people of Wyoming want to keep it that way. (Off my soap box.)