You could start with arriving at Bangalore for this city is well connected to many places in India. Spend two full days in Bangalore covering Lalbagh, Bangalore palace, Isckon temple, Tipu sultan summer palace, Vidhan soudha, planaterium, museum, Ulsoor lake, and few shopping places like MG road. From Bangalore Mysore is 4 hours away. You need a day in Mysore that from Mysore ooty is nearby. Two full days are much needed in this hill station whereby Coonoor needs half day covering. Coming back to Mysore you could cover hampi then take a bus back to Bangalore and fly to Kolkata. Each place travel takes about 5 to 6 hours so one or two days are much needed to cover each spot you have mentioned.
Hey, I can suggest you to follow this itinerary for visiting Bangalore, Coonoor, Ooty, Coorg, Mysore, and Hampi in 2 weeks: Day 1-2: Arrive in Bangalore and spend 2 days exploring the city. Visit popular attractions such as the ISKCON Temple, Tipu Sultan's Summer Palace, and the Bangalore Palace. Day 3-4: Take a train or bus to Coonoor, a hill station in the Nilgiri Hills. Enjoy the beautiful tea estates and take a toy train ride to Ooty. Day 5-6: Head to Ooty, another popular hill station in the Nilgiri Hills. Visit the Botanical Gardens, Doddabetta Peak, and take a ride on the Ooty Mountain Railway. Day 7-8: Travel to Coorg, a scenic hill town known for its coffee plantations and natural beauty. Take a tour of the coffee estates, visit the Abbey Falls and Raja's Seat. Day 9-10: Take a train or bus to Mysore and spend 2 days exploring the city. Visit the Mysore Palace, the Chamundi Hill, and the Brindavan Garden. Day 11-13: Take a train or bus to Hampi, a UNESCO World Heritage Site known for its ancient temples and ruins. Explore the Virupaksha Temple, the Vittala Temple Complex and the Monolithic statues of Ganesha and Nandi. Day 14: Return to Bangalore and depart Please note that this is just a suggested itinerary, and you may want to adjust it depending on your interests and the amount of time you have in each place. Happy Journey ✌️Hope it Helped.