Hi Mehak, Welcome to the Capital of India. You would surely enjoy the place.
I haven't heard of hostels much in Delhi. Still try looking at Zostel or Hostelworld app. Otherwise you can easily book an Oyo near CP as Connaught Place is the central hub to visit the entire Delhi. There is metro available and the station name is Rajiv Chowk. Roam around the CP circle at night, go for shopping, try new eateries or pubs. Take a metro, get down to Chandni Chowk and enjoy the place by travelling on foot. The place is famous for designer clothes at affordable prices, parantha wali Gali, natraj chaat house, lassi or falooda at giani and much more. If you eat non veg, take a rickshaw and head to Jama Masjid and try Karims, Aslam Butter Chicken, Qureshi kebabs and lots more. For Hauz khaas , you can get a metro easily. There are good pubs and a deer Park. Try out with the one having ladies night and enjoy the crowd over there . Have fun! Wish you a pleasant stay.
Zostel would be the best option to stay in Delhi. If you are a foodie, you must visit the JAMA Masjid road, you'll find hundreds of delicacies. Paranthe wali gali is a little overrated. But yeah, you can go shopping in CP, Hauz Khaas, Chandni chowk and Sarojini Nagar.
please visit Delhi, the travel won't be problem for visiting the places you have mentioned as metro is available best is you make a metro card for travelling for the same. there are a lot more places in Delhi that you should explore as well if you are a foodie and you are visiting Chandni Chowk, don't forget to visit the jama masjid for the delicacy and then you can find hotels in paharganj the metro station is R.K. Ashram Marg so you have to worry about food as street food and restaurants are there and it's near cp feel free to contact me if you need further information...
Prantha Gali is in CHnadani Chowk. keep a complete day for Chandandi Chowk. On Monday the market is closed Visit to Chandani Chowk : Gurudwara Sishganj, Jama Masjid, red fort , Paranthe vali gali, Natraj Dahi Balle, If u want to enjouy the party life visit Hauz khas village in evening time also u can cover hauz khaz fort near to it is qutub minar and sarojini market if u want to give ot a glance Cp is the heart of delhi which has many eateries, restarunts, and bars try getting food packed form kakke di hatti, enjoy icecream from naturals, visit janpath market for shopping, have time go to jhandewala mandir, near cp is bangla sahib gurudwara and india gate keep a day for this too