The only place that will accomodate the size of the Monty is the Fishing Bridge campground in the middle of Yellowstone. The other campgrounds are too small for your rig. Fortunately, it is one of the only campgrounds that allow reservations and you should consider getting one. The campsites there are packed tight but I hope you can find a spot.
(removed the travel comments, because they were not correct) Try this link for mucho information:
http://www.yellowstonepark.com/
On edit: I just checked the web link I provided and all but one of the campgrounds are closed this time of year and I don't know if the one that is still open (Mammoth CG) will accomodate your Monty. I recommend staying at the west entrance, because there are several campgrounds, including KOA that are open. I highly recommend you locate a place to stay versus just driving there hoping to get lucky, since dragging the Monty around looking for a place to stay can get frustrating especially in winter precipation.
HAVE FUN out there. Send us some pictures, LOL!