I want to go to Haridwar from Delhi. Which is the fastest and cheapest way to reach there? Also I want to know which are the must visit places there and nearby to it?
The best way to get there is an overnight train ride by Mussoorie Express which is fully booked at this time for general class but you can get a foreign quota ticket for any day since there are four tickets available daily. BTW, this train doesn't depart from New Delhi station but from Delhi Sarai Rohilla.
You can also get a bus for 300 rupees but I would definitely advise against it as it was horrible for me in a non-AC bus (maybe AC one is better). Also, you will probably get charged 350 to 400 rupees for that aforementioned ticket.
Nearby places that you should visit are Rishikesh, famous for temples and adventure activities such as rafting, kayaking, bungee etc. and Rajaji National Park that is pretty close to Haridwar but it gets expensive if you want a safari trip there.
Taking a train to Haridwar is surely the best option. The road to it, NH 58, is still being worked on and some kilometres of it are in a complete mess. So the best you can do is avoid it altogether.
There are many trains to Haridwar, almost all of these taking around 7 hours. One of the best trains to the place is Shatabdi and Jan Shatabdi, which leaves New Delhi Railway Station at around 3 in the afternoon and reaches Haridwar by 7.30 in the evening. You can take this one and rest for the night before hitting it off the next day. Mussoorie Express is another good option, taking which you'll reach Haridwar at around 6 am. Though there's an airport at Dehradun, it does not see many flights.
There are a number of temples in the city, which are considerably revered by the Hindus. Especially the hilltop temples of Mansa Devi and Chandi Devi, for which which you can take a ropeway. You can also visit the main market and watch the Ganga Arti that takes places every evening at Hari Ki Paudi.
Some other places near Haridwar are Rajaji Nationa Park, Dehradun, Rishikesh, Mussoorie and Lansdowne.