Here are the possible threads and the times they will happen (it is possible to be in more than one if the timing doesn't overlap):
1a) Go to the Hanamizuki Temple and try to make a deal with the priests (sometime tomorrow)
1b) Break into the Hanamizuki Temple and try to steal some peach wood (probably tonight)
2) take a trip down the mountain in search of the abandoned peach farm, hoping there is a tree or two left (all day tomorrow)
3) Astrally project back to the park to see if there are any signs left to be found (tonight, pretty much now)
4) Go to the university to track down and speak with the professor of occult studies (tomorrow at 3)
5) other (feel free to suggest any other things you may want to try instead if you have some useful ideas)