First thing I'd want to do is use the alarm key to make sure the alarms are on. Then go investigate.
There are eight characters to question, so by splitting up they should be able to question them all in two hours and have enough time left to look over four rooms. The rooms appear to be: Spaulding, Hackenbush, kitchen, Driftwood, electrical closet, Hammer, Miller, Wagstaff, Firefly, the security room, the idol room, the grand hall, the banquet hall, the entryway, and the back garden with its exit (I'm not sure if any of the unnamed rooms are the same as one of the named rooms, could a witch clarify this and maybe give a definitive list of what rooms are available to investigate?). With no other information, I'd say that the idol room, security room, electrical closet, and maybe the back garden with its exit would be at the top of my list to investigate. But that might change depending on what people say, so might as well just say the first thing we'll do and adjust based on the outcome.
I'd say Judgment talks to the Page of Swords, and Justice talks to the Knight of Swords, (two characters we haven't seen yet) to get things started, unless anyone has other suggestions.
Edit: just noticed that Flamebirde did make another suggestion. I think we'll probably want to talk to all the characters and investigate the idol room regardless, so I'll go with Flamebirde's suggestion of talking to Nine and investigating the idol room. And just add the step of making sure the alarms are on first.