We usually stay at hotels which is luxury but for a traveler it turns out to be expensive and waste of money. So i would rather suggest you to stay at any hostel ( zostel / the hostellers is recommended in rishikesh) which is cheaper and it helps you to interact with other travelers as well . So staying at a hostel can cost you Rs. 400-450 per night per person.
It would be better if you eat something from small shops or small hotels but make sure they are hygienic.
If you are a "the beatles" fan than you have to visit this cafe which is named after them , near laxman jhula.
So approximately you will be spending Rs 800-1000 in food.
4. Transportation in city
Traveling within the city can be cheaper if you travel by local transports such as local buses, Vikrams ( in uttrakhand) , sharing auto. It will hardly cost you approximately Rs. 400-500 .
Other expenses such as shopping , yoga classes , healing classes depends on the individual and his/her interest.
Let's calculate the overall expenses -
1. Transportation (delhi - rishikesh- delhi) = Rs 560
2. Stay (hostels for 3 days 2 nights) = Rs 800
3. Food (eat healthy and sufficient) = Rs. 1000
4. Transportation in city ( auto rikshaws / local buses) = Rs. 500
So within Rs. 3000 you can travel and explore rishikesh. Now go on and travel to the mountains.