Hi. For August September,places like Rajasthan-Delhi-Agra would be a good circuit to cover. If you want to go to the mountains, Leh Ladakh and Spiti are also good options.
You could visit these spots
Leh Ladakh
Srinagar
Some parts of north east like Meghalaya, Sikkim, Manipur
Kerala Karnataka and Maharashtra for rains come down during these months. Jaipur Udaipur Jaisalmer
Coorg Ooty Igatpuri Matheran hill stations
Goa Gokarna Pondicherry.