I myself have traveled to these places: Binsar, Chakrata these are couple of roads that will be mesmerizing if you travel there. Other than this: Kantala, Kausani are also recommended.
Hi Vivek,
The famous places you can visit are, Nainital, Dehradun, Mussoorie, Rishikesh, Haridwar. These places have good roads for a bike trip. You can also check this link to plan your trip to Uttarakhand - https://www.tripoto.com/uttarakhand?params=%7B%7D
Hope this helps.
Since you're planning to go in bike you can go Rishikesh next Dehradun next Mussoorie
next Dhanaulti
in between Dehradun and Mussoorie do plant to visit Robbers cave