Need help with affordable lodging Aug 1- Aug 9

Hi everyone. It's been almost 30 years since my last trip to Yellowstone when I was 16 and my wife has never been. I am planning a trip for the dates mentioned and need some wisdom on how to save some money on lodging. Is there any lodging deals or nice but budget friendly places to stay in the park or close by?

Also what area is the best to stay? I know the park is huge and I'd rather not have to drive any more than I have to. I'm not sure where most of the major attractions are other than Old Faithful in the center of the park. We will most likely have a rental car. No kids just the wife and me. We are driving in from Salt Lake City most likely

Thanks!!