With Dussehra coming in a weeks time, Mysore is one such spot to visit. Either first two days you see the celebration or last two days you view the celebrations. There are flights from chennai or Bangalore to Mysore, or from Bangalore you could hop on to a bus. Another way is trains from Bangalore. If you are planning 4 days stay in Mysore, book via Airbnb or Oyo now for as days near to Dussehra comes, rates hike up. You could cover Chamundi temple, rail museum, Brindavan gardens, bonsai garden, karanji lake, ranganathithu sanctuary and edmuri falls. One day is much needed to view the Dussehra celebration. Don’t forget to taste Mysore delicacies best sold around the palace..
From Mysore 3 hours away is Ooty. If you are planning for two days here are some important places, Ooty lake, botanical gardens, Dolphin nose, Doddabetta peak, Kalhatti falls. If you have few more days in hand, plan for trekking, hiking, Coonoor, wenlock downs, Pykara and tea factory visits. To stay there are lot of resorts around the lake, which are economical. Kindly check via MMT or Yatra.
Here are some tripoto links, which might help you plan your trip better.
https://www.tripoto.com/mysore/trips/amazing-trip-5dc81a79b1b3ahttps://www.tripoto.com/india/trips/mysore-to-ooty-scenic-journey-56f0e07544381https://www.tripoto.com/tamil-nadu/trips/a-short-trip-4365