Hi Pratik, the cost would depend upon your mode of transport and your city of origin, also the hotels you are staying in. if you travel in public transport and stay in hostels and budget hotels you can conclude your trip in under 4000 plus the charges of travelling form your city of origin to Chennai. Here is a list of places you must consider visiting:
Marina Beach Fort St. George
Arignar Anna Zoological Park
Valluvar Kottam Ashtalakshmi Temple, Kalikambal Temple