My wife and I would like to visit Japan for about 12-14 days.We are retired and in good shape.
When are the best times to go(With the temps high 60's to low 80's)?
Do we need a tour, if so which do you recommend ?
We would like to spend 3 days in Tokyo and 4 in Kyoto. What else are musts?

Check weather here: http://www.weatherbase.com

For a first round: Take a look at Tauck's itineraries and then think about duplicating or approximating a duplication of their itinerary to be done on your own. You can revise from there. The planning may help you decide if you want to spring for a tour or (my preference) do it on your own using Japan's excellent rail service.

You do not need a tour. Nor would I use a tour itinerary to plan my itinerary as tours are notorious for rushing you through places. What is a must for me may not be a must for you. Do some research. The best online resource is www.japan-guide.com They give some sample itineraries for you to consider.

Think about whether you might want to go to see the sakura (cherry blossoms) or koyo (fall colors). We went in November and had fine weather and the colors were incredible: www.marlandc.com/Japan-2013

My favourite time to visit Japan is cherry blossom season. It is just so beautiful everywhere and the Japanese are happiest when they are viewing the blossoms.

We spent three weeks in November of 2008 and they were spectacular. We very much want to return for sakura--but the cherry blossom season is briefer, and seems to involve less advance planning. We are glad that we chose the autumn--all three weeks were spectacular. You can find photos by clicking my name and seeing (extensive) trip report, one part of which is all autumn photos.

p.s. I strongly agree that a tour is neither necessary nor desirable.

I would spend the second week venturing where less tourists go. Tokyo and Kyoto are nice, but you will see many tourists there. I would choose a general area for the second week, and then I would stay in two different cities in that region. My two suggestions would be: The San'In Region, where I would divide my time between Tottori and Matsue. Alternatively, I would head down to the island of Kyushu and stay in Nakasaki and Kumamoto.

Most people will tell you to go in the autumn to see the changing leaves, or the spring to see the cherry blossoms, but it is difficult to time your visit exactly, as the weather patterns change every year. I personally like to go in September, just after Labor Day, when the European travelers have gone home. The weather is generally pleasant then as well.

Japan is the very easy to travel around on your own. The train system is amazing, and the people are so helpful. Many people I met wanted to draw me a diagram or map--that's the way they have been taught since they were born.