Looks like May 3, 4 and 5 are National holidays in Japan.
Tokyo, Kyoto, Himeji Castle and Mt. Fuji would have to be highlights, but there are so many other
places to see and things to do.
For 2 weeks in Japan, I would suggest a 1 week JR pass which currently costs about 28,300 YEN.
Check out http://gojapan.about.com/od/airtravel/a/japanairpass.htm
It gives info on discount domestic airfares on JAL and ANA for overseas visitors to Japan, and it gets better if you are
flying into Japan on a 'oneworld' or 'star alliance' airline.
Well worth a look and it might only cost about $100 USD to fly to Hiroshima from Tokyo if booked outside Japan (getting to Haneda airport from downtown Tokyo is a breeze).
If I was back in Japan for 2 weeks in May I'd -
spend 2 days in Tokyo on arrival
Fly to Hiroshima for 1-2 days then activate my railpass at Hiroshima station
Shinkansen to Himeji (3-4 hours would be enough) the on to Kyoto.
Himeji castle is one of the major sights of Japan. Kyoto was amazing. Did dinner in upstairs outdoors restaurant in Gion
which wasn't cheap. Next day did the LP walking tour of shrines/temples followed by the Gion walking tour at dusk and night. Visited Nijo-jo, the Golden Pavilion and the Silver Pavilion before leaving the next morning for Takayama in the Japanese Alps. Stayed 2 nights (nice town with old architecture and some nice temples) then bussed through Alps to Matsumoto for the medieval castle (almost rivals Himeji) and the Ukiyoe museum (great).
Railpassed from Matsumoto down to Otski and private train to Kawaguchi-ko train station at base of Fuji. Had booked the Sunnide Hotel ($130 AUD double room) but it does cheaper for backpackers (about $80 AUD, I think).
Fuji might be pretty busy in May even after holidays but an awesome sight if the weather is clear.
You could use railpass to get from Kyoto-Nagoya-Takayama then bus through to Matsumoto then Fuji (see above).
You can catch a bus from Kawaguchi-ko back to Tokyo but I bussed down to ??? and took the Shinkansen back to Tokyo cause I love riding that train so so much!!!
One place I really liked back in 83 was Kamakura. Easy train ride fom Tokyo and nice place to stay (big Buddha) with nice walks through hillside temples.
Tokyo's sights I visited were -
Shinjuku - views from 41st? floor of Metropolitan building and the nightlife of east Shinjuku (bars, restaurants, crazy
street punk bands)
Shibuya - my favourite place - have an evening coffee in Starbucks overlooking the station and watch the people cross the road and bars and standup sushi bars and cheap noodle shops and....
Harajuku - gotta go on a sunday afternoon and watch the crazy makeovers plus the rockers dancing close by and Yoyogi Park beside the railway station
Senso-ji Temple
Try http://www.japan-guide.com/event/ cause it looks as though the Sumo tournament is on in Tokyo from May 10-24 and the Sanja Matsuri Shinto festival in Tokyo May 15-17.
Sanja Matsuri Festival is known as one of the top festivals in Tokyo. The main feature of the festival is the parade of about a hundred mikoshi (portable shrines) by Ujiko (inhabitants of the neighbouring community) at Asakusa Shrine. A couple millions of people come to the festival every year.
Enjoy.
Anthony