yellowstone park-i want to camp in one place, where should I

Here is a link to the campground in YNP that allow generators.
Here

I would go ahead and call to see if you can get in at Fishing Bridge and continue to check periodically for cancellations.

I think if you get to the campgrounds early enough in morning you may be able to get a space. (except FB)

If you've never been there you're in for a treat.
If you HAVE been there you're still in for a treat.

Have fun!