Rishikesh is the place to be if you're looking for something adventurous. You can stay in Hostels(Mustache,Zostel,etc) for upto 300bucks(dorm rooms with ac) and they cost only 500Rs for 16km River Rafting(Cliff diving included).They charge 3550Rs for Bungee and Giant Swing each. There are also great treks like Chandrashila ,Roopkund,Har ki Dun ,Valley of Flowers. Rishikesh also has a great religious importance. Attend the Ganga Aarti at Triveni Ghar at 6pm. Hope you found this informative!
Ghaziabad is a central location . Most hill station in Uttrakhand will lie within the radius of 700 Km. However since you have a pre-decided budget I will recommend that you can do 3-4 day trip to Mussoorie and Dehradun . You can travel by bus or train. Reasonable budget accommodation will be available . Weather at both these places in March will be very nice.
You can do Manali, Rishikesh, Lucknow, Amritsar or even Jaipur and Ajmer. Totally depends on what kind of trip or location you are looking at. Manali, Amritsar and Rishikesh are mostly nature related while Lucknow is culture and food on the other hand Jaipur is all about history and architecture.
There are plenty of options from Ghaziabad. I myself put up at Ghaziabad and am a budget Traveller. Give more information for detailed information like your purpose of traveling, adventure, leisure or anything else, mode of transportation preferred and how many days.