Hi Aniket. Start from Rishikesh, head to Dehradun and then Mussoorie. See if you can visit Landour (about 6 km from Mussoorie - I had walked up all the way to Landour and back when I was in Mussoorie, it's a lovely walk). I'd say include Dhanaulti if possible (about 35 km Dehradun) and then go to Rudraprayag. Also, keep at least one buffer day in case you love any of these places and want to spend some more time, you easily can.