Where you stay depends on what you can afford to pay. Highest prices are within the park and the lowest are on east side several miles outside the park. Do some research on motel booking sites to find the best fit for you. We stayed in the town of Yellowstone just outside the west entrance to the park and the town is a quirky place and wish there was more time to explore it. We spent only one day there and it was not enough. If I had known that the entrance fee to the park was good for several days or maybe a week, don't quite remember which, things would have been planned differently. Also, the entrance fee was also good for at least another park, not sure but I think it was the Grand Tetons. Check the park website for more and better details.
What you have listed as places to go would be too much to do in a week and seems like at least 2 weeks or more of exploring would be better and more relaxing unless you want to rush from place to place and through each place you visit.
PS: Yellowstone was amazing, beautiful, and didn't have a life extinction event while we were there.