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Can anyone recommend the best route to take and the best travel options for getting around?

This will depend on your interests, so you'd need to tell us a bit more about what made you come to Japan.

Generally the easiest for getting around is by train for long distance transport and whatever public transport options there are for local transport (bus or subway/train usually). If you are on a budget, often highway buses for the long distance transport work out cheaper (but are less comfortable and usually take longer than trains). There are also various rail passes available, but you'd first need a rough idea about where you want to go before you consider what pass to get.

My general recommendation would be to spend about one week for Kyoto and Tokyo (both places would be a must for me) and to spend the other week elsewhere somewhere around central Honshu or on daytrips from Kyoto/Tokyo. Some popular places include the Alps: Matsumoto, Tsumago/Magome, Takayama, Shirakawago, Kanazawa. Popular day or overnight trips are: Nara from Kyoto or Kamakura/Nikko/Hakone/Kawaguchiko from Tokyo. Hiroshima+Miyajima is another popular destination.

I recommend to browse the thorntree archive which has plenty of 2 week itineraries, Japan Guide, JNTO, your guidebook and any other material you have/find on Japan in order to get an idea on what you might like.

You might be able to catch some cherry blossom. At that time of the year, that would likely happen in mountaineous areas of central Honshu (e.g. Kawaguchiko) or lowlands of Tohoku/Hokkaido. Some late blossoming species might even be in bloom in lowland central Honshu (e.g. at Kyoto's Ninna-ji).

Other than that I recommend to visit a festival or two. There are festivals all year round in many places of Japan, so finding one should not be a problem. Two famous and big ones which might fall into your travel period are the one in Takayama and Aoi Festival in Kyoto. If going to the one in Takayama you need to book accommodation ASAP. Also Kyoto accommodation will be busy during festivals, but there you could always commute from Osaka, so early booking is not that essential. Festivals in April