Efficient Itinary for 10 days in Japan?

Hi, I am arriving Tokyo on 9 Apr (morning) and intend to stay till 18th Apr (evening).

For this short trip, I intend to be in Tokyo, Osaka and Kyoto. Can anyone suggest what is the most efficient itinary for such a short stay?

9: arrive in Tokyo
10: Tokyo
11: Tokyo
12: Tokyo
13: train or bus ride to Kyoto
14: Kyoto
15: Kyoto
16: Kyoto
17: Osaka
18: depart Japan through Osaka's Kansai Airport

Depending on personal interests, you might want to change the duration of stay for the three cities.

Hi Uji,

Thank you for your prompt response.
I will arrive in Tokyo and have to fly out from Tokyo too.

Can you be more specific as in which places in Tokyo or in Kyoto or in Osaka I have to visit in order to experience Japan in such a short trip?

My initial plan:
Day 1: Tokyo
Day 2: Kyoto
Day 3: Kyoto
Day 4: Kyoto

Day 5:Kyoto
Day 6:Osaka
Day 7:Osaka/Tokyo
Day 8:Tokyo
Day 9:Tokyo
Day 10: Tokyo/ Home sweet home

Can you be more specific on which places I should visit in those cities.

You should pick according to your personal interests! The ratings on the following pages help you distinguish must-see spots (2-3 starts) from nice-to-see spots (0-1 stars).

Sights in Tokyo:
http://www.japan-guide.com/e/e2164.html

Sights in Kyoto:
http://www.japan-guide.com/e/e2158.html

Sights in Osaka:
http://www.japan-guide.com/e/e2157.html

I've always found Uji's responses helpful. You might check with your airline. When I've visited there has been no penalty for flying into Narita and out from Kansai (or visa versa - from the USA, anyway)
May I add a couple suggestions? Do try to visit onsen. In the cities the public baths can be very nice, in the countryside they can be sublime. There are a few rules - listed elsewhere. Men and Women are separated, and nude (but the only place I've felt more private is on my own home).
In Tokyo the Tsijiki Fish Market is amazing and I believe Kabuki-za has performances until the end of April before a 4 year renovation). Kyoto is a great 2nd choice. Much older and more traditional but still a city. Temples and palaces abound. Do try to get out of the city; Kabune is a lovely town an easy 30 minute train ride aay. Oh, I hope you will stay in a few ryokan. Some are more prepared to accept western visitors than others. Even the "ryokan hotels" can be fun,
Hope this helps!