We've stayed at Lake Yellowstone Lodge - nice place, but a not much to do at night. But you don't really need anything to do at night. We have also stayed at the Canyon cabins. Very rustic (read R-U-S-T-I-C!!!!), but still not bad. We stayed at Old Faithful Lodge in a room in the addition. This room was a little more modern and the OFI was really nice. (Picture Wilderness Lodge, but older and real). We also stayed in the Snow Lodge at OF in the winter. Had a cabin here and it was NEAT!!!!! 25 degrees below zero during the day and 45 below at night. We also did Mammoth Hot Springs Lodge (not the main lodge, but the add-on) in the winter and had elk right outside our window. This is where the students who work there during the summer stay during the summer months.
Stay at Old Faithful Lodge(darn, I'm getting mixed up between the Inn and Lodge, but you want the one that looks like Wilderness Lodge) in an addition room - not the bunk bed rooms, they are from the 1800's. Drive where you want to go each day. It's centrally located and you can hit West Yellowstone to see the Bear Park or Grand Tetons south of the park. You can drive over the mountains to go to Red Lodge, MT from there easily.
If you get there in late May, some of the roads may still be closed from winter snow. The lake doesn't thaw until Memorial Day or later. And the roads start closing again in September.
It's really easy to drive all the way around in a day. Or just hit the area you want in a day.