From.Delhi go to Haridwar by bus or train and then Visit to Rishikesh which is near about 25kms from.Haridwar. After that travel for 50km to Dehradun ,atlast go to Massoorie.
Also if you have more time then Visit Nainital, Ranikhet.
You can think like the following :
Day 1 : Reach Kathgodam and proceed for seetlakhet. Enroute visit Ranikhet.
Day 2: Seetlakhet to Kausani
Day 3 : Kausani to Chaukori
Day 4 : Chaukori to Munsiyari. Day 5: Munsiyari
Day 6 : Munsiyari to Dhaulchina
Day 7 : Dhaulchina to Binsar
Day 8 : Binsar to Mukteshwar
Day 9 : Mukteshwar to Nainital
Day 10 : Nainital
Day 11 : From Kathgodam take return train
you can easily take a comfortable and happening trip in this duration of time.
you can go to the following places... I assume that u r starting from Delhi...
Haridwar (must see is the Ganga Aarti)
Rishikesh (rafting and riverside camping)
Nainital (good for sightseeing and boatiing)
Mukteshwar ( trekking)
Kanatal , Tehri ,dhanaulti
all these places are nearby can easily be covered in 8-10 days...
for budget friendly options... 1: opt for public transport and trains
2 : stay at hostels or home stays.
3: have food at local dhabas
Perfect choice to visit uttakhand, if you are solo and don't want to hire any travelling agency or guide then you can visit dehradun,rishikesh and haridwar you can visit these place with your limit budget with no guide requirement and you can get easy navigation from the locals about the best places to visit near by.
You can plan to visit Kotdwar and lansidwon with your budget. if you are planning to visit chamoli,uttarakhand then I can provide you solo guide with best reasonable prices. you can quote your budget and I'll provide best visit destination according to your budget Mail me on firstname.lastname@example.org for more information