If you are keen on sakura viewing b33tlejuice, then you absolutely must go to Myougi San. The whole mountain is FULL of cherry blossoms, plum blossoms, azalea....The hike is a little hard, but the pot of gold at the end of that rainbow is well worth it.
Having been up to Mount Fuji twice, I can't say as that I'd recommend it, as there are other much more interesting mountains.
All the same, if you want to do any of the outdoors stuff like Mount Fuji or some such, checking the weather is really important. Probably a flexible schedule will be a good thing to have, and if the weather looks like it's good, then off you go!
Rounding all that up at the end of the day with an onsen is just heaven!