Step 1: Identify the Toda community.
The Toda are a small indigenous tribal group known for their unique pastoral culture, buffalo-rearing traditions, and embroidered shawls called Putkuli.
Step 2: Locate their homeland.
The Toda people primarily inhabit the Nilgiri Hills (the Blue Mountains) in Tamil Nadu, southern India, where they have lived for centuries.
Step 3: Eliminate wrong options.
The Satpura, Aravalli, and Vindhya ranges are located in central and western India and have no primary association with the Toda community.
\[ \boxed{\text{Nilgiris Hills}} \]