Leave early morning from your destination without bath, reach Haridwar take bath,have some brkfast and roam in local market and leave for rishikesh check in there, have lunch there and take some rest in evening go to near by temples,visit evening prayers seat near ghat.Next day go for water activities,paintball, treasure hunt etc at night do bonfire and enjoy barbeque dinner and take full rest.Next day leave for mussoorie take room for 2 days enjoy there,one day local mall road,2nd day near by attraction like garden,lake,kempty fall etc.Next day leave for dhanolti or kanatal both of them are amazing places,away from city rush enjoy peace and do want ever you want to do enjoy 2 days there and then leave for dehradun enjoy 3 days,there are lot of local attraction there so you need good time there to cover most of them and then in night leave for your home as per your destination.
so in total =day in haridwar+2 days in rishikesh+2 days in mussoorie+2days in dhanolti/kanatal+3 days in dehradun=8-9 days
Leave from delhi around 12am-1am, You will reach rishikesh in 5 hours.
Day1: first thing in morning- rafting, explore laxman jhula, go to beatles cafe for amazing coffee, by evening, attend the aarti by ghat. Day 2 night: leave afterwards if you not intend to stay for more at rishikesh, Dehradhun is 1.5 hours of drive from rishikesh. sleep off that night. get up in the morning. Paragliding for some adventure
Explore rajaji national park
Tapkeshwar Temple Day 3: not sure if you like to trek, if you do then, go for nag tibba trek. max 4 hours trek. enjoy the trek, come back. rest (that's all for day 3) Day 4: you can enjoy local market: Paltan Bazzar, Tibetan Market and Tiger Falls too. Call it a day and leave for Massoorie. Day 5: Go for beautiful mussoorie lake, afterwards check out the mall road, if possible go for Jwalaji Temple same day otherwise, leave it for the next. Day 6: Cable car ride & sky bridge and leave for delhi, it will be drive of 8 hours max (depending upon the traffic) if you have any doubts or want to say anything, drop a message on instagram: _banjaaran__: https://www.instagram.com/_banjaaran__/ Happy Travelling!!
You can start with rishikesh, spend 2 days there camping, the best one will be pebbles resort on neelkanth route, you can take my name for discounts. there you can do river rafting the next day and visit neelkanth temple and explore city, then proceed towards mussoorie for 2 days and while returning you can explore ddn and then Haridwar while on your way back then back to Delhi. this is the best route to save time.
Arrive to Haridwar and visit all some places in Nearly 2 days , dont miss the Har ki Paudi Aarti in evening . After that go to Rishikesh (25kms from Haridwar) which you can visit in around 2 days with temples and Rafting. After that should go to Dehradun which is nearly 50kms from Rishikesh and at the end go Massoorie.
You have not mentioned anything about your transportation. Assuming that you would be reaching uttarakhand by air, I think starting from Dehradun is okay then you move other places accordingly. If you are reaching Uttarakhand by train then start form haridwar
If your are going there 4 beautiful place so it's really going to good experience, first you have to start your trip at night that's why u will reach Haridwar in morning then take gangasnan visit neelkanth, chandi devi mandir and mansa devi mandir then at night join the ganga aarti.
Day 2 will start from shantikunj and from there leave haridwar to rishikesh. In Rishikesh u have to try laxman jhula and 2 adventures sports ( Rafting & Bungee Jumping) In evening u have to leave rishikesh to dehradun and stay there in night. Day 3 will start in Dehradun .There are several spots in Dehradun but u must have to go F.R.I. u will see the natural beauti there. day 4 will still going in dehradun.
Day 5 , Day 6 U will stay in Masoori and there are really natural beauti, hills, waterfalls etc. will attract you. Day 7 trip will over .