Accommodation is between 3 and 10 pounds everywhere.... Yes, you can also spend 20-100, but there is no need. There are higher priced hotels in Manali than there are in Vashist. Dharamsala caters to movie stars so there is defineitley high end, but head up towards mcloud ganj and prices drop..
For Manali, as soon as you arrive in Delhi, book a night bus to Manali. Leaves 6 pm arrives about 11 am next day. From there, vashist with its hotsprings is 10 mintues by rickshaw or a walk of 45 minutes. Vashisht is touristy, but still great. Pass the days hiking all over, hot springs, visiting manali, eating, and Acclimatizing.. etc. Doesnt matter whether you stay in Manali or Vashist, pro's and cons to both. 2400meters
From Manali/Vashist, its very easy to take an overnight car/tax/bus to Dharamsala if you want. For me, i'd first go to kibber and kaza which is part of Spiti valley for a very unique part of India. Read up on Kibber and Kaza. Its a mini tibet in many ways, very isolated but amazing with some great places to see. Stay one night in Kaza to acclimatize, 3600 meters, then go up to kibber for a few days, 4000 meters plus. DO NOT underestimate the acclimatization. Some will say its boring, but totally different place and well above tree line. From there you can continue the loop to Shimla and head to Dharamsala, or can go back to Vashist and Dharamsala that way as well. You might also consider from Dharamsala a last stop in Amristar, to see the golden temple and then last train back to Delhi. Three weeks is easily doable for all this, but it is a fair amount of travel. IMOP, Shimla is nothing special but still have to throw it out there.
Happy travels...August is a great time to be in the north of india