The road is 700H, after the Nautilus a little way. Follow this road past the first pullout/campsite and trend right when it begins to "Y" Party Dome will be right in front of you when you are in the second parking lot.
Couple of us refer to it as "Rodeo [pronounced "ro-DAY-oh"] Rock," owing to a large contingent of cowboys who were there in situ during one particular Frontier Days week. Not that it would be any more appropos. My kids call it "that rock we climbed."