General:
* Hint
* Tip
* Indication
* Signal
* Evidence
* Trace
* Lead
* Intimation
* Suggestion
* Pointer
More specific:
* For solving a mystery:
* Evidence
* Proof
* Proof positive
* Key
* Solution
* For understanding something:
* Insight
* Explanation
* Key
* Solution
* For something that is obvious:
* Giveaway
* Dead giveaway
* Sign
* Telltale sign
The best synonym to use will depend on the specific situation and the meaning you want to convey.