For dehradun, rishikesh& mussourie, i will definately help you for planning your trip, if u are crazy for trekking, bike trip, then u enjoy much more than u can imagine, there are various trekking sites, in mussourie like george everest(place where british officer george everest used to live, his house is also there with a very beautiful view of city dehradun)&also the george everest peak is next to awesome, cloud end, company park, mall road, central library,kempty fall ,bhtta fall , shikhar fall,dhanolti, lal tibba (point frm where u can see himalayas) & so many beautiful places tht i cant explain this way, About dehradun, city situated in base of mussourie, where u can find numerous no. of spots like robbers cave , malsi deer Park, santla Devi river, and many more ..
Rishikesh- this place is full of peace like several ganga river sides , shri Ram jhula , shri Laxman jhula, u can feel nature there , as there are several jungle view sides too where there are so many falls too. as I suggest u should visit there at once ..
enjoy Summer n dont forget to try water games there ...
It is a messy itinerary. Since all the cities are long distance, your days will go in travelling, you will not be able to enjoy the trip at all. Choose either Pondicherry, Gokarna, Mumbai or the other 3.
Some cities are in North where some in South. Your most of the time will waste in Travelling. Because all cities are far from each other and if you want to reach in quick way Flight is the only option. My suggestion is either adopt only north or south side and explore that one side in fullest. Have a Happy travelling !