Step 1: Identify the meaning. The sentence is about preference of a newspaper. The word "eldest" is used for the "oldest among brothers/sisters," not for "children" in general.
Step 2: Correct usage. In standard English, the correct word is "elder" when referring to sons/daughters. "Eldest" is only for the oldest among more than two siblings.
Step 3: Rewrite. The correct sentence should be:
"I prefer The Hindu, but my elder son reads The Times of India."
\[
\boxed{\text{Wrong word: eldest}}
\]