I will be travelling to Japan in May for roughly 10 days. Given that it is such a short amount of time what cities or attractions would you recommend are a 'must'? I've travelled Europe and South East Asia but this will be my first time in Japan so need a little help navigating.
Nothing is a "must see"...or at least it varies from person to person...but the vast majority of first timers with that timeframe probably go to Tokyo and Kyoto.
As lucapal says, there is nothing in Japan that is 'must see.' No particular temple, mountain, museum or sight that you have to visit to say you have been to Japan.
With 10 days most people would split time between Kanto(Tokyo) and Kansai(Kyoto) or focus on one with a slew of day trips, jaunts to the surrounding areas.
Where are you flying in and out of?
What are your interests generally?
What led you to book a trip to Japan?
Are you traveling during the large national holiday in early May?
What is 'roughly 10 day?' Is that 8 nights? 12 days? exactly 240 hours? Flying from Toronto with the associated jet lag?

I will be flying from Toronto and it will most likely be 10-12 days including jetlag. I haven't checked booked the ticket yet as I wasn't sure what would be the best airport to fly into.
Japan is on the bucket list so its mainly just to sight see. and vacation.
You should be able to get an open jaw ticket for roughly same price as a straight return.
That will save you time and money backtracking...

Thanks...this is very helpful. What sites would you recommend for booking the ticket?
Have a look at a consolidator,like Skyscanner.
That will show you most possibilities and give you links to the airlines and online travel agents which offer the flights.