Personally, the Shiratani trail is more beautiful than the Jomon Sugi trail. If you have time, do both. Else, Shiratani is an easier and nicer trail, with many big cedar trees as well.
Good thing about Yakushima trail is that you don't need good weather as most of the trail are within the forest with little opportunity to view the landscape of nearby mountains (except Toikawa Rock). If fact, the moss gets more vibrant after a rain.
We did the Bugyosugi Cedar Course plus Toikawa Rock loop, which should take 4 hours, but we spend the entire day in Shiratani (from 8am) and left on the last bus at 4.10pm.
This is a pretty small place, with the main attraction is the section of the gorge with waterfall. The place for boating is narrow and limited, and walking trail is pretty short.
We get up close to the crater to view loads of poisonous gas spitting out from the crater, and occasionally you can view the blue color water at the bottom of the crater.
The crater is pretty sensitive, as you might have to wait until the gas level is low enough to have a safe viewing near the edge of the crater.
The walking path around the crater is off limit during my visit.
Raizan trail is certainly much beautiful than Homanzan, though weather is cloudy. Sadly we didn't have enough time to cross to Iharayama peak as well and do a return loop.
Going to Canal City Hakata, they have a musical water fountain and light show going on occasionally.
The best part of the garden is Koi watching, which can only be done outside of the tea room (do we didn't go for the tea). Entrance is 200 yen.