What do you want in your hotel room or vacation rental? If you want to be in the park the Lake hotel, the lodge at Old Faithful or the Mammoth Hotel are all amazing. For the best park experience split your time between them.
However, you won't get things like television, wifi, multiple dining options, fast food, shopping etc. And you will pay dearly. Outside the park, you won't have the ambiance of being in Yellowstone, but you can get those creature comforts and better pricing. It only takes a few minutes to go from the gateway towns into the park if you get up early. If I was going to vacation by hotel I would stay a couple of days in West Yellowstone, a couple of days in Gardiner, a couple of days in Jackson (Grand Teton Park) and maybe two days in Silvergate/Cooke City (for the animals in the Lamar Valley). That would have me close to new places every couple of days but still in civilization. But I am in to creature comforts and enjoy turning on the TV after a long day and am not really into paying double cost for a bad hamburger at one of the restaurants inside the park. For me, packing and unpacking a suitcase is worth it to not have long, repetitive drives.