I`ll be crossing my fingers for you on the sakura bit. Plum blossoms are already in bloom here, and from what I understand it`s going to be abnormally warm this spring - which means the sakura may very well be done and gone by the time you get here.
The average for Tokyo appears to be the last week of March, first week of April - so anything earlier than normal and you`ll miss out.

There are no free buses from the airport, but prices are reasonable. Tours are good ways to see a lot in a short period of time, but prices can vary.

As to what to see in Yokohama, it depends on what you are in to.