Fantastic place - lucky enough to have spent a few days there twice in the last few years.
If you want to stay overnight in park-run accommodation then book as far in advance as you can; otherwise plenty of lodging immediately outside park gates especially the west gate. Choice of eateries there too but be sure to get IN and OUT the park gates v v early to avoid queues. So much wildlife and geological phenomena to see there, just wonderful. But PLAN your route and activities - the park is closed through Oct - May as climate is severe. Is the BBC series in 3 episodes (shown a few years back)? If so be sure to see the one on winter and how wildlife survives months of sub-zero temperatures and several feet of snow.

If I knew how to attach photos I'd attach a few to illustrate what you can get close to. And if anyone wants further tips, then feel free to PM me.